/* Subroutine */ int csscal_(integer *n, real *sa, complex *cx, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1;
/* Local variables */
integer i__, nincx;
/* Purpose */
/* ======= */
/* scales a complex vector by a real constant. */
/* jack dongarra, linpack, 3/11/78. */
/* modified 3/93 to return if incx .le. 0. */
/* modified 12/3/93, array(1) declarations changed to array(*) */
/* Parameter adjustments */
--cx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
i__3 = i__;
i__4 = i__;
r__1 = *sa * cx[i__4].r;
r__2 = *sa * r_imag(&cx[i__]);
q__1.r = r__1, q__1.i = r__2;
cx[i__3].r = q__1.r, cx[i__3].i = q__1.i;
}
return 0;
/* code for increment equal to 1 */
L20:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = i__;
i__3 = i__;
r__1 = *sa * cx[i__3].r;
r__2 = *sa * r_imag(&cx[i__]);
q__1.r = r__1, q__1.i = r__2;
cx[i__1].r = q__1.r, cx[i__1].i = q__1.i;
}
return 0;
} /* csscal_ */
/* Complex */ VOID cladiv_(complex * ret_val, complex *x, complex *y)
{
/* -- LAPACK auxiliary routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
CLADIV := X / Y, where X and Y are complex. The computation of X / Y
will not overflow on an intermediary step unless the results
overflows.
Arguments
=========
X (input) COMPLEX
Y (input) COMPLEX
The complex scalars X and Y.
=====================================================================
*/
/* System generated locals */
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static real zi, zr;
extern /* Subroutine */ int sladiv_(real *, real *, real *, real *, real *
, real *);
r__1 = x->r;
r__2 = r_imag(x);
r__3 = y->r;
r__4 = r_imag(y);
sladiv_(&r__1, &r__2, &r__3, &r__4, &zr, &zi);
q__1.r = zr, q__1.i = zi;
ret_val->r = q__1.r, ret_val->i = q__1.i;
return ;
/* End of CLADIV */
} /* cladiv_ */
doublereal scabs1_(complex *z__)
{
/* System generated locals */
real ret_val, r__1, r__2;
/* Purpose */
/* ======= */
/* SCABS1 computes absolute value of a complex number */
ret_val = (r__1 = z__->r, dabs(r__1)) + (r__2 = r_imag(z__), dabs(r__2));
return ret_val;
} /* scabs1_ */
/* DECK CGAMR */
/* Complex */ void cgamr_(complex * ret_val, complex *z__)
{
/* System generated locals */
complex q__1, q__2;
/* Local variables */
static real x;
static integer irold;
extern /* Subroutine */ int xgetf_(integer *), xsetf_(integer *);
extern /* Complex */ void clngam_(complex *, complex *);
extern /* Subroutine */ int xerclr_(void);
/* ***BEGIN PROLOGUE CGAMR */
/* ***PURPOSE Compute the reciprocal of the Gamma function. */
/* ***LIBRARY SLATEC (FNLIB) */
/* ***CATEGORY C7A */
/* ***TYPE COMPLEX (GAMR-S, DGAMR-D, CGAMR-C) */
/* ***KEYWORDS FNLIB, RECIPROCAL GAMMA FUNCTION, SPECIAL FUNCTIONS */
/* ***AUTHOR Fullerton, W., (LANL) */
/* ***DESCRIPTION */
/* CGAMR(Z) calculates the reciprocal gamma function for COMPLEX */
/* argument Z. This is a preliminary version that is not accurate. */
/* ***REFERENCES (NONE) */
/* ***ROUTINES CALLED CLNGAM, XERCLR, XGETF, XSETF */
/* ***REVISION HISTORY (YYMMDD) */
/* 770701 DATE WRITTEN */
/* 861211 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* ***END PROLOGUE CGAMR */
/* ***FIRST EXECUTABLE STATEMENT CGAMR */
ret_val->r = 0.f, ret_val->i = 0.f;
x = z__->r;
if (x <= 0.f && r_int(&x) == x && r_imag(z__) == 0.f) {
return ;
}
xgetf_(&irold);
xsetf_(&c__1);
clngam_(&q__1, z__);
ret_val->r = q__1.r, ret_val->i = q__1.i;
xerclr_();
xsetf_(&irold);
q__2.r = - ret_val->r, q__2.i = - ret_val->i;
c_exp(&q__1, &q__2);
ret_val->r = q__1.r, ret_val->i = q__1.i;
return ;
} /* cgamr_ */
real scabs1_(complex *z__)
{
/* System generated locals */
real ret_val, r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SCABS1 computes absolute value of a complex number */
/* .. Intrinsic Functions .. */
/* .. */
ret_val = (r__1 = z__->r, dabs(r__1)) + (r__2 = r_imag(z__), dabs(r__2));
return ret_val;
} /* scabs1_ */
/* Subroutine */ int clatrs_(char *uplo, char *trans, char *diag, char *
normin, integer *n, complex *a, integer *lda, complex *x, real *scale,
real *cnorm, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j;
real xj, rec, tjj;
integer jinc;
real xbnd;
integer imax;
real tmax;
complex tjjs;
real xmax, grow;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
real tscal;
complex uscal;
integer jlast;
extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
complex csumj;
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
logical upper;
extern /* Subroutine */ int ctrsv_(char *, char *, char *, integer *,
complex *, integer *, complex *, integer *), slabad_(real *, real *);
extern integer icamax_(integer *, complex *, integer *);
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), xerbla_(char *, integer *);
real bignum;
extern integer isamax_(integer *, real *, integer *);
extern doublereal scasum_(integer *, complex *, integer *);
logical notran;
integer jfirst;
real smlnum;
logical nounit;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLATRS solves one of the triangular systems */
/* A * x = s*b, A**T * x = s*b, or A**H * x = s*b, */
/* with scaling to prevent overflow. Here A is an upper or lower */
/* triangular matrix, A**T denotes the transpose of A, A**H denotes the */
/* conjugate transpose of A, x and b are n-element vectors, and s is a */
/* scaling factor, usually less than or equal to 1, chosen so that the */
/* components of x will be less than the overflow threshold. If the */
/* unscaled problem will not cause overflow, the Level 2 BLAS routine */
/* CTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), */
/* then s is set to 0 and a non-trivial solution to A*x = 0 is returned. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies the operation applied to A. */
/* = 'N': Solve A * x = s*b (No transpose) */
/* = 'T': Solve A**T * x = s*b (Transpose) */
/* = 'C': Solve A**H * x = s*b (Conjugate transpose) */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* NORMIN (input) CHARACTER*1 */
/* Specifies whether CNORM has been set or not. */
/* = 'Y': CNORM contains the column norms on entry */
/* = 'N': CNORM is not set on entry. On exit, the norms will */
/* be computed and stored in CNORM. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading n by n */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading n by n lower */
/* triangular part of the array A contains the lower triangular */
/* matrix, and the strictly upper triangular part of A is not */
/* referenced. If DIAG = 'U', the diagonal elements of A are */
/* also not referenced and are assumed to be 1. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max (1,N). */
/* X (input/output) COMPLEX array, dimension (N) */
/* On entry, the right hand side b of the triangular system. */
/* On exit, X is overwritten by the solution vector x. */
/* SCALE (output) REAL */
/* The scaling factor s for the triangular system */
/* A * x = s*b, A**T * x = s*b, or A**H * x = s*b. */
/* If SCALE = 0, the matrix A is singular or badly scaled, and */
/* the vector x is an exact or approximate solution to A*x = 0. */
/* CNORM (input or output) REAL array, dimension (N) */
/* If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */
/* contains the norm of the off-diagonal part of the j-th column */
/* of A. If TRANS = 'N', CNORM(j) must be greater than or equal */
/* to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */
/* must be greater than or equal to the 1-norm. */
/* If NORMIN = 'N', CNORM is an output argument and CNORM(j) */
/* returns the 1-norm of the offdiagonal part of the j-th column */
/* of A. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -k, the k-th argument had an illegal value */
/* Further Details */
/* ======= ======= */
/* A rough bound on x is computed; if that is less than overflow, CTRSV */
/* is called, otherwise, specific code is used which checks for possible */
/* overflow or divide-by-zero at every operation. */
/* A columnwise scheme is used for solving A*x = b. The basic algorithm */
/* if A is lower triangular is */
/* x[1:n] := b[1:n] */
/* for j = 1, ..., n */
/* x(j) := x(j) / A(j,j) */
/* x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */
/* end */
/* Define bounds on the components of x after j iterations of the loop: */
/* M(j) = bound on x[1:j] */
/* G(j) = bound on x[j+1:n] */
/* Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. */
/* Then for iteration j+1 we have */
/* M(j+1) <= G(j) / | A(j+1,j+1) | */
/* G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */
/* <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */
/* where CNORM(j+1) is greater than or equal to the infinity-norm of */
/* column j+1 of A, not counting the diagonal. Hence */
/* G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */
/* 1<=i<=j */
/* and */
/* |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */
/* 1<=i< j */
/* Since |x(j)| <= M(j), we use the Level 2 BLAS routine CTRSV if the */
/* reciprocal of the largest M(j), j=1,..,n, is larger than */
/* max(underflow, 1/overflow). */
/* The bound on x(j) is also used to determine when a step in the */
/* columnwise method can be performed without fear of overflow. If */
/* the computed bound is greater than a large constant, x is scaled to */
/* prevent overflow, but if the bound overflows, x is set to 0, x(j) to */
/* 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */
/* Similarly, a row-wise scheme is used to solve A**T *x = b or */
/* A**H *x = b. The basic algorithm for A upper triangular is */
/* for j = 1, ..., n */
/* x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j) */
/* end */
/* We simultaneously compute two bounds */
/* G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j */
/* M(j) = bound on x(i), 1<=i<=j */
/* The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we */
/* add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */
/* Then the bound on x(j) is */
/* M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */
/* <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */
/* 1<=i<=j */
/* and we can safely call CTRSV if 1/M(n) and 1/G(n) are both greater */
/* than max(underflow, 1/overflow). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--cnorm;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
/* Test the input parameters. */
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (! lsame_(normin, "Y") && ! lsame_(normin,
"N")) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLATRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine machine dependent parameters to control overflow. */
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum /= slamch_("Precision");
bignum = 1.f / smlnum;
*scale = 1.f;
if (lsame_(normin, "N")) {
/* Compute the 1-norm of each column, not including the diagonal. */
if (upper) {
/* A is upper triangular. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
cnorm[j] = scasum_(&i__2, &a[j * a_dim1 + 1], &c__1);
/* L10: */
}
} else {
/* A is lower triangular. */
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
cnorm[j] = scasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1);
/* L20: */
}
cnorm[*n] = 0.f;
}
}
/* Scale the column norms by TSCAL if the maximum element in CNORM is */
/* greater than BIGNUM/2. */
imax = isamax_(n, &cnorm[1], &c__1);
tmax = cnorm[imax];
if (tmax <= bignum * .5f) {
tscal = 1.f;
} else {
tscal = .5f / (smlnum * tmax);
sscal_(n, &tscal, &cnorm[1], &c__1);
}
/* Compute a bound on the computed solution vector to see if the */
/* Level 2 BLAS routine CTRSV can be used. */
xmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j;
r__3 = xmax, r__4 = (r__1 = x[i__2].r / 2.f, dabs(r__1)) + (r__2 =
r_imag(&x[j]) / 2.f, dabs(r__2));
xmax = dmax(r__3,r__4);
/* L30: */
}
xbnd = xmax;
if (notran) {
/* Compute the growth in A * x = b. */
if (upper) {
jfirst = *n;
jlast = 1;
jinc = -1;
} else {
jfirst = 1;
jlast = *n;
jinc = 1;
}
if (tscal != 1.f) {
grow = 0.f;
goto L60;
}
if (nounit) {
/* A is non-unit triangular. */
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
/* Initially, G(0) = max{x(i), i=1,...,n}. */
grow = .5f / dmax(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
i__3 = j + j * a_dim1;
tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj >= smlnum) {
/* M(j) = G(j-1) / abs(A(j,j)) */
/* Computing MIN */
r__1 = xbnd, r__2 = dmin(1.f,tjj) * grow;
xbnd = dmin(r__1,r__2);
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.f;
}
if (tjj + cnorm[j] >= smlnum) {
/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */
grow *= tjj / (tjj + cnorm[j]);
} else {
/* G(j) could overflow, set GROW to 0. */
grow = 0.f;
}
/* L40: */
}
grow = xbnd;
} else {
/* A is unit triangular. */
/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
/* Computing MIN */
r__1 = 1.f, r__2 = .5f / dmax(xbnd,smlnum);
grow = dmin(r__1,r__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
/* G(j) = G(j-1)*( 1 + CNORM(j) ) */
grow *= 1.f / (cnorm[j] + 1.f);
/* L50: */
}
}
L60:
;
} else {
/* Compute the growth in A**T * x = b or A**H * x = b. */
if (upper) {
jfirst = 1;
jlast = *n;
jinc = 1;
} else {
jfirst = *n;
jlast = 1;
jinc = -1;
}
if (tscal != 1.f) {
grow = 0.f;
goto L90;
}
if (nounit) {
/* A is non-unit triangular. */
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
/* Initially, M(0) = max{x(i), i=1,...,n}. */
grow = .5f / dmax(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */
xj = cnorm[j] + 1.f;
/* Computing MIN */
r__1 = grow, r__2 = xbnd / xj;
grow = dmin(r__1,r__2);
i__3 = j + j * a_dim1;
tjjs.r = a[i__3].r, tjjs.i = a[i__3].i;
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj >= smlnum) {
/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
if (xj > tjj) {
xbnd *= tjj / xj;
}
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.f;
}
/* L70: */
}
grow = dmin(grow,xbnd);
} else {
/* A is unit triangular. */
/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
/* Computing MIN */
r__1 = 1.f, r__2 = .5f / dmax(xbnd,smlnum);
grow = dmin(r__1,r__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = ( 1 + CNORM(j) )*G(j-1) */
xj = cnorm[j] + 1.f;
grow /= xj;
/* L80: */
}
}
L90:
;
}
if (grow * tscal > smlnum) {
/* Use the Level 2 BLAS solve if the reciprocal of the bound on */
/* elements of X is not too small. */
ctrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1);
} else {
/* Use a Level 1 BLAS solve, scaling intermediate results. */
if (xmax > bignum * .5f) {
/* Scale X so that its components are less than or equal to */
/* BIGNUM in absolute value. */
*scale = bignum * .5f / xmax;
csscal_(n, scale, &x[1], &c__1);
xmax = bignum;
} else {
xmax *= 2.f;
}
if (notran) {
/* Solve A * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
if (nounit) {
i__3 = j + j * a_dim1;
q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3].i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L105;
}
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale x by 1/b(j). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */
/* to avoid overflow when dividing by A(j,j). */
rec = tjj * bignum / xj;
if (cnorm[j] > 1.f) {
/* Scale by 1/CNORM(j) to avoid overflow when */
/* multiplying x(j) times column j. */
rec /= cnorm[j];
}
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0, and compute a solution to A*x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L100: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
xj = 1.f;
*scale = 0.f;
xmax = 0.f;
}
L105:
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j of A. */
if (xj > 1.f) {
rec = 1.f / xj;
if (cnorm[j] > (bignum - xmax) * rec) {
/* Scale x by 1/(2*abs(x(j))). */
rec *= .5f;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
} else if (xj * cnorm[j] > bignum - xmax) {
/* Scale x by 1/2. */
csscal_(n, &c_b36, &x[1], &c__1);
*scale *= .5f;
}
if (upper) {
if (j > 1) {
/* Compute the update */
/* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) */
i__3 = j - 1;
i__4 = j;
q__2.r = -x[i__4].r, q__2.i = -x[i__4].i;
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
caxpy_(&i__3, &q__1, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
i__3 = j - 1;
i__ = icamax_(&i__3, &x[1], &c__1);
i__3 = i__;
xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__]), dabs(r__2));
}
} else {
if (j < *n) {
/* Compute the update */
/* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) */
i__3 = *n - j;
i__4 = j;
q__2.r = -x[i__4].r, q__2.i = -x[i__4].i;
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
caxpy_(&i__3, &q__1, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
i__3 = *n - j;
i__ = j + icamax_(&i__3, &x[j + 1], &c__1);
i__3 = i__;
xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__]), dabs(r__2));
}
}
/* L110: */
}
} else if (lsame_(trans, "T")) {
/* Solve A**T * x = b */
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Compute x(j) = b(j) - sum A(k,j)*x(k). */
/* k<>j */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
uscal.r = tscal, uscal.i = 0.f;
rec = 1.f / dmax(xmax,1.f);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5f;
if (nounit) {
i__3 = j + j * a_dim1;
q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3]
.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > 1.f) {
/* Divide by A(j,j) when scaling x if A(j,j) > 1. */
/* Computing MIN */
r__1 = 1.f, r__2 = rec * tjj;
rec = dmin(r__1,r__2);
cladiv_(&q__1, &uscal, &tjjs);
uscal.r = q__1.r, uscal.i = q__1.i;
}
if (rec < 1.f) {
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0.f, csumj.i = 0.f;
if (uscal.r == 1.f && uscal.i == 0.f) {
/* If the scaling needed for A in the dot product is 1, */
/* call CDOTU to perform the dot product. */
if (upper) {
i__3 = j - 1;
cdotu_(&q__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
} else if (j < *n) {
i__3 = *n - j;
cdotu_(&q__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
q__3.r = a[i__4].r * uscal.r - a[i__4].i *
uscal.i, q__3.i = a[i__4].r * uscal.i + a[
i__4].i * uscal.r;
i__5 = i__;
q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i,
q__2.i = q__3.r * x[i__5].i + q__3.i * x[
i__5].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L120: */
}
} else if (j < *n) {
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * a_dim1;
q__3.r = a[i__4].r * uscal.r - a[i__4].i *
uscal.i, q__3.i = a[i__4].r * uscal.i + a[
i__4].i * uscal.r;
i__5 = i__;
q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i,
q__2.i = q__3.r * x[i__5].i + q__3.i * x[
i__5].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L130: */
}
}
}
q__1.r = tscal, q__1.i = 0.f;
if (uscal.r == q__1.r && uscal.i == q__1.i) {
/* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
/* was not used to scale the dotproduct. */
i__3 = j;
i__4 = j;
q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i -
csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
if (nounit) {
i__3 = j + j * a_dim1;
q__1.r = tscal * a[i__3].r, q__1.i = tscal * a[i__3]
.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L145;
}
}
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0 and compute a solution to A**T *x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L140: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
*scale = 0.f;
xmax = 0.f;
}
L145:
;
} else {
/* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
/* product has already been divided by 1/A(j,j). */
i__3 = j;
cladiv_(&q__2, &x[j], &tjjs);
q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
/* Computing MAX */
i__3 = j;
r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[j]), dabs(r__2));
xmax = dmax(r__3,r__4);
/* L150: */
}
} else {
/* Solve A**H * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Compute x(j) = b(j) - sum A(k,j)*x(k). */
/* k<>j */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
uscal.r = tscal, uscal.i = 0.f;
rec = 1.f / dmax(xmax,1.f);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5f;
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > 1.f) {
/* Divide by A(j,j) when scaling x if A(j,j) > 1. */
/* Computing MIN */
r__1 = 1.f, r__2 = rec * tjj;
rec = dmin(r__1,r__2);
cladiv_(&q__1, &uscal, &tjjs);
uscal.r = q__1.r, uscal.i = q__1.i;
}
if (rec < 1.f) {
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0.f, csumj.i = 0.f;
if (uscal.r == 1.f && uscal.i == 0.f) {
/* If the scaling needed for A in the dot product is 1, */
/* call CDOTC to perform the dot product. */
if (upper) {
i__3 = j - 1;
cdotc_(&q__1, &i__3, &a[j * a_dim1 + 1], &c__1, &x[1],
&c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
} else if (j < *n) {
i__3 = *n - j;
cdotc_(&q__1, &i__3, &a[j + 1 + j * a_dim1], &c__1, &
x[j + 1], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
r_cnjg(&q__4, &a[i__ + j * a_dim1]);
q__3.r = q__4.r * uscal.r - q__4.i * uscal.i,
q__3.i = q__4.r * uscal.i + q__4.i *
uscal.r;
i__4 = i__;
q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
q__2.i = q__3.r * x[i__4].i + q__3.i * x[
i__4].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L160: */
}
} else if (j < *n) {
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
r_cnjg(&q__4, &a[i__ + j * a_dim1]);
q__3.r = q__4.r * uscal.r - q__4.i * uscal.i,
q__3.i = q__4.r * uscal.i + q__4.i *
uscal.r;
i__4 = i__;
q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
q__2.i = q__3.r * x[i__4].i + q__3.i * x[
i__4].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L170: */
}
}
}
q__1.r = tscal, q__1.i = 0.f;
if (uscal.r == q__1.r && uscal.i == q__1.i) {
/* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
/* was not used to scale the dotproduct. */
i__3 = j;
i__4 = j;
q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i -
csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L185;
}
}
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0 and compute a solution to A**H *x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L180: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
*scale = 0.f;
xmax = 0.f;
}
L185:
;
} else {
/* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
/* product has already been divided by 1/A(j,j). */
i__3 = j;
cladiv_(&q__2, &x[j], &tjjs);
q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
/* Computing MAX */
i__3 = j;
r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[j]), dabs(r__2));
xmax = dmax(r__3,r__4);
/* L190: */
}
}
*scale /= tscal;
}
/* Scale the column norms by 1/TSCAL for return. */
if (tscal != 1.f) {
r__1 = 1.f / tscal;
sscal_(n, &r__1, &cnorm[1], &c__1);
}
return 0;
/* End of CLATRS */
} /* clatrs_ */
/* Subroutine */ int cherfs_(char *uplo, integer *n, integer *nrhs, complex *
a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr,
complex *work, real *rwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CHERFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefinite, and
provides error bounds and backward error estimates for the solution.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) COMPLEX array, dimension (LDAF,N)
The factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by CHETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CHETRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters
===================
ITMAX is the maximum number of steps of iterative refinement.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer kase;
static real safe1, safe2;
static integer i__, j, k;
static real s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), ccopy_(integer *, complex *, integer *, complex *,
integer *), caxpy_(integer *, complex *, complex *, integer *,
complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
static real xk;
extern doublereal slamch_(char *);
static integer nz;
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), chetrs_(
char *, integer *, integer *, complex *, integer *, integer *,
complex *, integer *, integer *);
static real lstres, eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHERFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - A * X */
ccopy_(n, &b_ref(1, j), &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = 0.f;
chemv_(uplo, n, &q__1, &a[a_offset], lda, &x_ref(1, j), &c__1, &c_b1,
&work[1], &c__1);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th components of the
numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
b_ref(i__, j)), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = x_subscr(k, j);
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(k,
j)), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = a_subscr(i__, k);
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a_ref(i__, k)), dabs(r__2))) * xk;
i__4 = a_subscr(i__, k);
i__5 = x_subscr(i__, j);
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
a_ref(i__, k)), dabs(r__2))) * ((r__3 = x[i__5].r,
dabs(r__3)) + (r__4 = r_imag(&x_ref(i__, j)),
dabs(r__4)));
/* L40: */
}
i__3 = a_subscr(k, k);
rwork[k] = rwork[k] + (r__1 = a[i__3].r, dabs(r__1)) * xk + s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = x_subscr(k, j);
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(k,
j)), dabs(r__2));
i__3 = a_subscr(k, k);
rwork[k] += (r__1 = a[i__3].r, dabs(r__1)) * xk;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = a_subscr(i__, k);
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a_ref(i__, k)), dabs(r__2))) * xk;
i__4 = a_subscr(i__, k);
i__5 = x_subscr(i__, j);
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
a_ref(i__, k)), dabs(r__2))) * ((r__3 = x[i__5].r,
dabs(r__3)) + (r__4 = r_imag(&x_ref(i__, j)),
dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
chetrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x_ref(1, j), &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula
norm(X - XTRUE) / norm(X) .le. FERR =
norm( abs(inv(A))*
( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(A) is the inverse of A
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(A)*abs(X) + abs(B) is less than SAFE2.
Use CLACON to estimate the infinity-norm of the matrix
inv(A) * diag(W),
where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &work[*n + 1], &work[1], &ferr[j], &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
chetrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
chetrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = x_subscr(i__, j);
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x_ref(i__, j)), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CHERFS */
} /* cherfs_ */
/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *
ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer *
ldx, real *ferr, real *berr, complex *work, real *rwork, integer *
info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s;
integer kk;
real xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern /* Subroutine */ int cgbmv_(char *, integer *, integer *, integer *
, integer *, complex *, complex *, integer *, complex *, integer *
, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
integer count;
extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
*, integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), cgbtrs_(
char *, integer *, integer *, integer *, integer *, complex *,
integer *, integer *, complex *, integer *, integer *);
logical notran;
char transn[1], transt[1];
real lstres;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGBRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is banded, and provides */
/* error bounds and backward error estimates for the solution. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose) */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The original band matrix A, stored in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input) COMPLEX array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by CGBTRF. U is stored as an upper triangular band */
/* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/* the multipliers used during the factorization are stored in */
/* rows KL+KU+2 to 2*KL+KU+1. */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from CGBTRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CGBTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -5;
} else if (*ldab < *kl + *ku + 1) {
*info = -7;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -9;
} else if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGBRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
/* Computing MIN */
i__1 = *kl + *ku + 2, i__2 = *n + 1;
nz = min(i__1,i__2);
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
cgbmv_(trans, n, n, kl, ku, &q__1, &ab[ab_offset], ldab, &x[j *
x_dim1 + 1], &c__1, &c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
kk = *ku + 1 - k;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
/* Computing MAX */
i__3 = 1, i__4 = k - *ku;
/* Computing MIN */
i__6 = *n, i__7 = k + *kl;
i__5 = min(i__6,i__7);
for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) {
i__3 = kk + i__ + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[kk + i__ + k * ab_dim1]), dabs(r__2)))
* xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
kk = *ku + 1 - k;
/* Computing MAX */
i__5 = 1, i__3 = k - *ku;
/* Computing MIN */
i__6 = *n, i__7 = k + *kl;
i__4 = min(i__6,i__7);
for (i__ = max(i__5,i__3); i__ <= i__4; ++i__) {
i__5 = kk + i__ + k * ab_dim1;
i__3 = i__ + j * x_dim1;
s += ((r__1 = ab[i__5].r, dabs(r__1)) + (r__2 = r_imag(&
ab[kk + i__ + k * ab_dim1]), dabs(r__2))) * ((
r__3 = x[i__3].r, dabs(r__3)) + (r__4 = r_imag(&x[
i__ + j * x_dim1]), dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__4 = i__;
r__3 = s, r__4 = ((r__1 = work[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__4 = i__;
r__3 = s, r__4 = ((r__1 = work[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
, &work[1], n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(op(A)))* */
/* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(op(A)) is the inverse of op(A) */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(op(A)) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__4 = i__;
rwork[i__] = (r__1 = work[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__4 = i__;
rwork[i__] = (r__1 = work[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
cgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
ipiv[1], &work[1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__4 = i__;
i__5 = i__;
i__3 = i__;
q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5]
* work[i__3].i;
work[i__4].r = q__1.r, work[i__4].i = q__1.i;
/* L110: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__4 = i__;
i__5 = i__;
i__3 = i__;
q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5]
* work[i__3].i;
work[i__4].r = q__1.r, work[i__4].i = q__1.i;
/* L120: */
}
cgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
ipiv[1], &work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__4 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CGBRFS */
} /* cgbrfs_ */
/* Subroutine */ int clalsa_(integer *icompq, integer *smlsiz, integer *n,
integer *nrhs, complex *b, integer *ldb, complex *bx, integer *ldbx,
real *u, integer *ldu, real *vt, integer *k, real *difl, real *difr,
real *z__, real *poles, integer *givptr, integer *givcol, integer *
ldgcol, integer *perm, real *givnum, real *c__, real *s, real *rwork,
integer *iwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
CLALSA is an itermediate step in solving the least squares problem
by computing the SVD of the coefficient matrix in compact form (The
singular vectors are computed as products of simple orthorgonal
matrices.).
If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector
matrix of an upper bidiagonal matrix to the right hand side; and if
ICOMPQ = 1, CLALSA applies the right singular vector matrix to the
right hand side. The singular vector matrices were generated in
compact form by CLALSA.
Arguments
=========
ICOMPQ (input) INTEGER
Specifies whether the left or the right singular vector
matrix is involved.
= 0: Left singular vector matrix
= 1: Right singular vector matrix
SMLSIZ (input) INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N (input) INTEGER
The row and column dimensions of the upper bidiagonal matrix.
NRHS (input) INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input) COMPLEX array, dimension ( LDB, NRHS )
On input, B contains the right hand sides of the least
squares problem in rows 1 through M. On output, B contains
the solution X in rows 1 through N.
LDB (input) INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,MAX( M, N ) ).
BX (output) COMPLEX array, dimension ( LDBX, NRHS )
On exit, the result of applying the left or right singular
vector matrix to B.
LDBX (input) INTEGER
The leading dimension of BX.
U (input) REAL array, dimension ( LDU, SMLSIZ ).
On entry, U contains the left singular vector matrices of all
subproblems at the bottom level.
LDU (input) INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR,
POLES, GIVNUM, and Z.
VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ).
On entry, VT' contains the right singular vector matrices of
all subproblems at the bottom level.
K (input) INTEGER array, dimension ( N ).
DIFL (input) REAL array, dimension ( LDU, NLVL ).
where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
DIFR (input) REAL array, dimension ( LDU, 2 * NLVL ).
On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
distances between singular values on the I-th level and
singular values on the (I -1)-th level, and DIFR(*, 2 * I)
record the normalizing factors of the right singular vectors
matrices of subproblems on I-th level.
Z (input) REAL array, dimension ( LDU, NLVL ).
On entry, Z(1, I) contains the components of the deflation-
adjusted updating row vector for subproblems on the I-th
level.
POLES (input) REAL array, dimension ( LDU, 2 * NLVL ).
On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
singular values involved in the secular equations on the I-th
level.
GIVPTR (input) INTEGER array, dimension ( N ).
On entry, GIVPTR( I ) records the number of Givens
rotations performed on the I-th problem on the computation
tree.
GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
locations of Givens rotations performed on the I-th level on
the computation tree.
LDGCOL (input) INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
On entry, PERM(*, I) records permutations done on the I-th
level of the computation tree.
GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ).
On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
values of Givens rotations performed on the I-th level on the
computation tree.
C (input) REAL array, dimension ( N ).
On entry, if the I-th subproblem is not square,
C( I ) contains the C-value of a Givens rotation related to
the right null space of the I-th subproblem.
S (input) REAL array, dimension ( N ).
On entry, if the I-th subproblem is not square,
S( I ) contains the S-value of a Givens rotation related to
the right null space of the I-th subproblem.
RWORK (workspace) REAL array, dimension at least
max ( N, (SMLSZ+1)*NRHS*3 ).
IWORK (workspace) INTEGER array.
The dimension must be at least 3 * N
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static real c_b9 = 1.f;
static real c_b10 = 0.f;
static integer c__2 = 2;
/* System generated locals */
integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1,
difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
z_dim1, z_offset, b_dim1, b_offset, bx_dim1, bx_offset, i__1,
i__2, i__3, i__4, i__5, i__6;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
integer pow_ii(integer *, integer *);
/* Local variables */
static integer jcol, nlvl, sqre, jrow, i__, j, jimag, jreal, inode, ndiml;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
static integer ndimr;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
static integer i1;
extern /* Subroutine */ int clals0_(integer *, integer *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
integer *, integer *, integer *, integer *, real *, integer *,
real *, real *, real *, real *, integer *, real *, real *, real *,
integer *);
static integer ic, lf, nd, ll, nl, nr;
extern /* Subroutine */ int xerbla_(char *, integer *), slasdt_(
integer *, integer *, integer *, integer *, integer *, integer *,
integer *);
static integer im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1;
#define difl_ref(a_1,a_2) difl[(a_2)*difl_dim1 + a_1]
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define perm_ref(a_1,a_2) perm[(a_2)*perm_dim1 + a_1]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define bx_subscr(a_1,a_2) (a_2)*bx_dim1 + a_1
#define bx_ref(a_1,a_2) bx[bx_subscr(a_1,a_2)]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_dim1 + a_1]
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
bx_dim1 = *ldbx;
bx_offset = 1 + bx_dim1 * 1;
bx -= bx_offset;
givnum_dim1 = *ldu;
givnum_offset = 1 + givnum_dim1 * 1;
givnum -= givnum_offset;
poles_dim1 = *ldu;
poles_offset = 1 + poles_dim1 * 1;
poles -= poles_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
difr_dim1 = *ldu;
difr_offset = 1 + difr_dim1 * 1;
difr -= difr_offset;
difl_dim1 = *ldu;
difl_offset = 1 + difl_dim1 * 1;
difl -= difl_offset;
vt_dim1 = *ldu;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
--k;
--givptr;
perm_dim1 = *ldgcol;
perm_offset = 1 + perm_dim1 * 1;
perm -= perm_offset;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1 * 1;
givcol -= givcol_offset;
--c__;
--s;
--rwork;
--iwork;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*smlsiz < 3) {
*info = -2;
} else if (*n < *smlsiz) {
*info = -3;
} else if (*nrhs < 1) {
*info = -4;
} else if (*ldb < *n) {
*info = -6;
} else if (*ldbx < *n) {
*info = -8;
} else if (*ldu < *n) {
*info = -10;
} else if (*ldgcol < *n) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLALSA", &i__1);
return 0;
}
/* Book-keeping and setting up the computation tree. */
inode = 1;
ndiml = inode + *n;
ndimr = ndiml + *n;
slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
smlsiz);
/* The following code applies back the left singular vector factors.
For applying back the right singular vector factors, go to 170. */
if (*icompq == 1) {
goto L170;
}
/* The nodes on the bottom level of the tree were solved
by SLASDQ. The corresponding left and right singular vector
matrices are in explicit form. First apply back the left
singular vector matrices. */
ndb1 = (nd + 1) / 2;
i__1 = nd;
for (i__ = ndb1; i__ <= i__1; ++i__) {
/* IC : center row of each node
NL : number of rows of left subproblem
NR : number of rows of right subproblem
NLF: starting row of the left subproblem
NRF: starting row of the right subproblem */
i1 = i__ - 1;
ic = iwork[inode + i1];
nl = iwork[ndiml + i1];
nr = iwork[ndimr + i1];
nlf = ic - nl;
nrf = ic + 1;
/* Since B and BX are complex, the following call to SGEMM
is performed in two steps (real and imaginary parts).
CALL SGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU,
$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */
j = nl * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
i__4 = b_subscr(jrow, jcol);
rwork[j] = b[i__4].r;
/* L10: */
}
/* L20: */
}
sgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u_ref(nlf, 1), ldu, &rwork[(
nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[1], &nl);
j = nl * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L30: */
}
/* L40: */
}
sgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u_ref(nlf, 1), ldu, &rwork[(
nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[nl * *nrhs + 1], &
nl);
jreal = 0;
jimag = nl * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nl - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = bx_subscr(jrow, jcol);
i__5 = jreal;
i__6 = jimag;
q__1.r = rwork[i__5], q__1.i = rwork[i__6];
bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L50: */
}
/* L60: */
}
/* Since B and BX are complex, the following call to SGEMM
is performed in two steps (real and imaginary parts).
CALL SGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */
j = nr * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
i__4 = b_subscr(jrow, jcol);
rwork[j] = b[i__4].r;
/* L70: */
}
/* L80: */
}
sgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u_ref(nrf, 1), ldu, &rwork[(
nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[1], &nr);
j = nr * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L90: */
}
/* L100: */
}
sgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u_ref(nrf, 1), ldu, &rwork[(
nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[nr * *nrhs + 1], &
nr);
jreal = 0;
jimag = nr * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nr - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = bx_subscr(jrow, jcol);
i__5 = jreal;
i__6 = jimag;
q__1.r = rwork[i__5], q__1.i = rwork[i__6];
bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L110: */
}
/* L120: */
}
/* L130: */
}
/* Next copy the rows of B that correspond to unchanged rows
in the bidiagonal matrix to BX. */
i__1 = nd;
for (i__ = 1; i__ <= i__1; ++i__) {
ic = iwork[inode + i__ - 1];
ccopy_(nrhs, &b_ref(ic, 1), ldb, &bx_ref(ic, 1), ldbx);
/* L140: */
}
/* Finally go through the left singular vector matrices of all
the other subproblems bottom-up on the tree. */
j = pow_ii(&c__2, &nlvl);
sqre = 0;
for (lvl = nlvl; lvl >= 1; --lvl) {
lvl2 = (lvl << 1) - 1;
/* find the first node LF and last node LL on
the current level LVL */
if (lvl == 1) {
lf = 1;
ll = 1;
} else {
i__1 = lvl - 1;
lf = pow_ii(&c__2, &i__1);
ll = (lf << 1) - 1;
}
i__1 = ll;
for (i__ = lf; i__ <= i__1; ++i__) {
im1 = i__ - 1;
ic = iwork[inode + im1];
nl = iwork[ndiml + im1];
nr = iwork[ndimr + im1];
nlf = ic - nl;
nrf = ic + 1;
--j;
clals0_(icompq, &nl, &nr, &sqre, nrhs, &bx_ref(nlf, 1), ldbx, &
b_ref(nlf, 1), ldb, &perm_ref(nlf, lvl), &givptr[j], &
givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2),
ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
s[j], &rwork[1], info);
/* L150: */
}
/* L160: */
}
goto L330;
/* ICOMPQ = 1: applying back the right singular vector factors. */
L170:
/* First now go through the right singular vector matrices of all
the tree nodes top-down. */
j = 0;
i__1 = nlvl;
for (lvl = 1; lvl <= i__1; ++lvl) {
lvl2 = (lvl << 1) - 1;
/* Find the first node LF and last node LL on
the current level LVL. */
if (lvl == 1) {
lf = 1;
ll = 1;
} else {
i__2 = lvl - 1;
lf = pow_ii(&c__2, &i__2);
ll = (lf << 1) - 1;
}
i__2 = lf;
for (i__ = ll; i__ >= i__2; --i__) {
im1 = i__ - 1;
ic = iwork[inode + im1];
nl = iwork[ndiml + im1];
nr = iwork[ndimr + im1];
nlf = ic - nl;
nrf = ic + 1;
if (i__ == ll) {
sqre = 0;
} else {
sqre = 1;
}
++j;
clals0_(icompq, &nl, &nr, &sqre, nrhs, &b_ref(nlf, 1), ldb, &
bx_ref(nlf, 1), ldbx, &perm_ref(nlf, lvl), &givptr[j], &
givcol_ref(nlf, lvl2), ldgcol, &givnum_ref(nlf, lvl2),
ldu, &poles_ref(nlf, lvl2), &difl_ref(nlf, lvl), &
difr_ref(nlf, lvl2), &z___ref(nlf, lvl), &k[j], &c__[j], &
s[j], &rwork[1], info);
/* L180: */
}
/* L190: */
}
/* The nodes on the bottom level of the tree were solved
by SLASDQ. The corresponding right singular vector
matrices are in explicit form. Apply them back. */
ndb1 = (nd + 1) / 2;
i__1 = nd;
for (i__ = ndb1; i__ <= i__1; ++i__) {
i1 = i__ - 1;
ic = iwork[inode + i1];
nl = iwork[ndiml + i1];
nr = iwork[ndimr + i1];
nlp1 = nl + 1;
if (i__ == nd) {
nrp1 = nr;
} else {
nrp1 = nr + 1;
}
nlf = ic - nl;
nrf = ic + 1;
/* Since B and BX are complex, the following call to SGEMM is
performed in two steps (real and imaginary parts).
CALL SGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
$ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */
j = nlp1 * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
i__4 = b_subscr(jrow, jcol);
rwork[j] = b[i__4].r;
/* L200: */
}
/* L210: */
}
sgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt_ref(nlf, 1), ldu, &
rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[1], &
nlp1);
j = nlp1 * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L220: */
}
/* L230: */
}
sgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt_ref(nlf, 1), ldu, &
rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[nlp1 * *
nrhs + 1], &nlp1);
jreal = 0;
jimag = nlp1 * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nlf + nlp1 - 1;
for (jrow = nlf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = bx_subscr(jrow, jcol);
i__5 = jreal;
i__6 = jimag;
q__1.r = rwork[i__5], q__1.i = rwork[i__6];
bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L240: */
}
/* L250: */
}
/* Since B and BX are complex, the following call to SGEMM is
performed in two steps (real and imaginary parts).
CALL SGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
$ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */
j = nrp1 * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
i__4 = b_subscr(jrow, jcol);
rwork[j] = b[i__4].r;
/* L260: */
}
/* L270: */
}
sgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt_ref(nrf, 1), ldu, &
rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[1], &
nrp1);
j = nrp1 * *nrhs << 1;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++j;
rwork[j] = r_imag(&b_ref(jrow, jcol));
/* L280: */
}
/* L290: */
}
sgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt_ref(nrf, 1), ldu, &
rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[nrp1 * *
nrhs + 1], &nrp1);
jreal = 0;
jimag = nrp1 * *nrhs;
i__2 = *nrhs;
for (jcol = 1; jcol <= i__2; ++jcol) {
i__3 = nrf + nrp1 - 1;
for (jrow = nrf; jrow <= i__3; ++jrow) {
++jreal;
++jimag;
i__4 = bx_subscr(jrow, jcol);
i__5 = jreal;
i__6 = jimag;
q__1.r = rwork[i__5], q__1.i = rwork[i__6];
bx[i__4].r = q__1.r, bx[i__4].i = q__1.i;
/* L300: */
}
/* L310: */
}
/* L320: */
}
L330:
return 0;
/* End of CLALSA */
} /* clalsa_ */
int chgeqz_(char *job, char *compq, char *compz, int *n,
int *ilo, int *ihi, complex *h__, int *ldh, complex *t,
int *ldt, complex *alpha, complex *beta, complex *q, int *ldq,
complex *z__, int *ldz, complex *work, int *lwork, float *
rwork, int *info)
{
/* System generated locals */
int h_dim1, h_offset, q_dim1, q_offset, t_dim1, t_offset, z_dim1,
z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
float r__1, r__2, r__3, r__4, r__5, r__6;
complex q__1, q__2, q__3, q__4, q__5, q__6;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
double r_imag(complex *);
void c_div(complex *, complex *, complex *), pow_ci(complex *, complex *,
int *), c_sqrt(complex *, complex *);
/* Local variables */
float c__;
int j;
complex s, t1;
int jc, in;
complex u12;
int jr;
complex ad11, ad12, ad21, ad22;
int jch;
int ilq, ilz;
float ulp;
complex abi22;
float absb, atol, btol, temp;
extern int crot_(int *, complex *, int *,
complex *, int *, float *, complex *);
float temp2;
extern int cscal_(int *, complex *, complex *,
int *);
extern int lsame_(char *, char *);
complex ctemp;
int iiter, ilast, jiter;
float anorm, bnorm;
int maxit;
complex shift;
float tempr;
complex ctemp2, ctemp3;
int ilazr2;
float ascale, bscale;
complex signbc;
extern double slamch_(char *), clanhs_(char *, int *,
complex *, int *, float *);
extern int claset_(char *, int *, int *, complex
*, complex *, complex *, int *), clartg_(complex *,
complex *, float *, complex *, complex *);
float safmin;
extern int xerbla_(char *, int *);
complex eshift;
int ilschr;
int icompq, ilastm;
complex rtdisc;
int ischur;
int ilazro;
int icompz, ifirst, ifrstm, istart;
int lquery;
/* -- LAPACK routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHGEQZ computes the eigenvalues of a complex matrix pair (H,T), */
/* where H is an upper Hessenberg matrix and T is upper triangular, */
/* using the single-shift QZ method. */
/* Matrix pairs of this type are produced by the reduction to */
/* generalized upper Hessenberg form of a complex matrix pair (A,B): */
/* A = Q1*H*Z1**H, B = Q1*T*Z1**H, */
/* as computed by CGGHRD. */
/* If JOB='S', then the Hessenberg-triangular pair (H,T) is */
/* also reduced to generalized Schur form, */
/* H = Q*S*Z**H, T = Q*P*Z**H, */
/* where Q and Z are unitary matrices and S and P are upper triangular. */
/* Optionally, the unitary matrix Q from the generalized Schur */
/* factorization may be postmultiplied into an input matrix Q1, and the */
/* unitary matrix Z may be postmultiplied into an input matrix Z1. */
/* If Q1 and Z1 are the unitary matrices from CGGHRD that reduced */
/* the matrix pair (A,B) to generalized Hessenberg form, then the output */
/* matrices Q1*Q and Z1*Z are the unitary factors from the generalized */
/* Schur factorization of (A,B): */
/* A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. */
/* To avoid overflow, eigenvalues of the matrix pair (H,T) */
/* (equivalently, of (A,B)) are computed as a pair of complex values */
/* (alpha,beta). If beta is nonzero, lambda = alpha / beta is an */
/* eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP) */
/* A*x = lambda*B*x */
/* and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the */
/* alternate form of the GNEP */
/* mu*A*y = B*y. */
/* The values of alpha and beta for the i-th eigenvalue can be read */
/* directly from the generalized Schur form: alpha = S(i,i), */
/* beta = P(i,i). */
/* Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix */
/* Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), */
/* pp. 241--256. */
/* Arguments */
/* ========= */
/* JOB (input) CHARACTER*1 */
/* = 'E': Compute eigenvalues only; */
/* = 'S': Computer eigenvalues and the Schur form. */
/* COMPQ (input) CHARACTER*1 */
/* = 'N': Left Schur vectors (Q) are not computed; */
/* = 'I': Q is initialized to the unit matrix and the matrix Q */
/* of left Schur vectors of (H,T) is returned; */
/* = 'V': Q must contain a unitary matrix Q1 on entry and */
/* the product Q1*Q is returned. */
/* COMPZ (input) CHARACTER*1 */
/* = 'N': Right Schur vectors (Z) are not computed; */
/* = 'I': Q is initialized to the unit matrix and the matrix Z */
/* of right Schur vectors of (H,T) is returned; */
/* = 'V': Z must contain a unitary matrix Z1 on entry and */
/* the product Z1*Z is returned. */
/* N (input) INTEGER */
/* The order of the matrices H, T, Q, and Z. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* ILO and IHI mark the rows and columns of H which are in */
/* Hessenberg form. It is assumed that A is already upper */
/* triangular in rows and columns 1:ILO-1 and IHI+1:N. */
/* If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. */
/* H (input/output) COMPLEX array, dimension (LDH, N) */
/* On entry, the N-by-N upper Hessenberg matrix H. */
/* On exit, if JOB = 'S', H contains the upper triangular */
/* matrix S from the generalized Schur factorization. */
/* If JOB = 'E', the diagonal of H matches that of S, but */
/* the rest of H is unspecified. */
/* LDH (input) INTEGER */
/* The leading dimension of the array H. LDH >= MAX( 1, N ). */
/* T (input/output) COMPLEX array, dimension (LDT, N) */
/* On entry, the N-by-N upper triangular matrix T. */
/* On exit, if JOB = 'S', T contains the upper triangular */
/* matrix P from the generalized Schur factorization. */
/* If JOB = 'E', the diagonal of T matches that of P, but */
/* the rest of T is unspecified. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= MAX( 1, N ). */
/* ALPHA (output) COMPLEX array, dimension (N) */
/* The complex scalars alpha that define the eigenvalues of */
/* GNEP. ALPHA(i) = S(i,i) in the generalized Schur */
/* factorization. */
/* BETA (output) COMPLEX array, dimension (N) */
/* The float non-negative scalars beta that define the */
/* eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized */
/* Schur factorization. */
/* Together, the quantities alpha = ALPHA(j) and beta = BETA(j) */
/* represent the j-th eigenvalue of the matrix pair (A,B), in */
/* one of the forms lambda = alpha/beta or mu = beta/alpha. */
/* Since either lambda or mu may overflow, they should not, */
/* in general, be computed. */
/* Q (input/output) COMPLEX array, dimension (LDQ, N) */
/* On entry, if COMPZ = 'V', the unitary matrix Q1 used in the */
/* reduction of (A,B) to generalized Hessenberg form. */
/* On exit, if COMPZ = 'I', the unitary matrix of left Schur */
/* vectors of (H,T), and if COMPZ = 'V', the unitary matrix of */
/* left Schur vectors of (A,B). */
/* Not referenced if COMPZ = 'N'. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= 1. */
/* If COMPQ='V' or 'I', then LDQ >= N. */
/* Z (input/output) COMPLEX array, dimension (LDZ, N) */
/* On entry, if COMPZ = 'V', the unitary matrix Z1 used in the */
/* reduction of (A,B) to generalized Hessenberg form. */
/* On exit, if COMPZ = 'I', the unitary matrix of right Schur */
/* vectors of (H,T), and if COMPZ = 'V', the unitary matrix of */
/* right Schur vectors of (A,B). */
/* Not referenced if COMPZ = 'N'. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1. */
/* If COMPZ='V' or 'I', then LDZ >= N. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO >= 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= MAX(1,N). */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* = 1,...,N: the QZ iteration did not converge. (H,T) is not */
/* in Schur form, but ALPHA(i) and BETA(i), */
/* i=INFO+1,...,N should be correct. */
/* = N+1,...,2*N: the shift calculation failed. (H,T) is not */
/* in Schur form, but ALPHA(i) and BETA(i), */
/* i=INFO-N+1,...,N should be correct. */
/* Further Details */
/* =============== */
/* We assume that complex ABS works as long as its value is less than */
/* overflow. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode JOB, COMPQ, COMPZ */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
--alpha;
--beta;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
/* Function Body */
if (lsame_(job, "E")) {
ilschr = FALSE;
ischur = 1;
} else if (lsame_(job, "S")) {
ilschr = TRUE;
ischur = 2;
} else {
ischur = 0;
}
if (lsame_(compq, "N")) {
ilq = FALSE;
icompq = 1;
} else if (lsame_(compq, "V")) {
ilq = TRUE;
icompq = 2;
} else if (lsame_(compq, "I")) {
ilq = TRUE;
icompq = 3;
} else {
icompq = 0;
}
if (lsame_(compz, "N")) {
ilz = FALSE;
icompz = 1;
} else if (lsame_(compz, "V")) {
ilz = TRUE;
icompz = 2;
} else if (lsame_(compz, "I")) {
ilz = TRUE;
icompz = 3;
} else {
icompz = 0;
}
/* Check Argument Values */
*info = 0;
i__1 = MAX(1,*n);
work[1].r = (float) i__1, work[1].i = 0.f;
lquery = *lwork == -1;
if (ischur == 0) {
*info = -1;
} else if (icompq == 0) {
*info = -2;
} else if (icompz == 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*ilo < 1) {
*info = -5;
} else if (*ihi > *n || *ihi < *ilo - 1) {
*info = -6;
} else if (*ldh < *n) {
*info = -8;
} else if (*ldt < *n) {
*info = -10;
} else if (*ldq < 1 || ilq && *ldq < *n) {
*info = -14;
} else if (*ldz < 1 || ilz && *ldz < *n) {
*info = -16;
} else if (*lwork < MAX(1,*n) && ! lquery) {
*info = -18;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHGEQZ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
/* WORK( 1 ) = CMPLX( 1 ) */
if (*n <= 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
/* Initialize Q and Z */
if (icompq == 3) {
claset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
}
if (icompz == 3) {
claset_("Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz);
}
/* Machine Constants */
in = *ihi + 1 - *ilo;
safmin = slamch_("S");
ulp = slamch_("E") * slamch_("B");
anorm = clanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &rwork[1]);
bnorm = clanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &rwork[1]);
/* Computing MAX */
r__1 = safmin, r__2 = ulp * anorm;
atol = MAX(r__1,r__2);
/* Computing MAX */
r__1 = safmin, r__2 = ulp * bnorm;
btol = MAX(r__1,r__2);
ascale = 1.f / MAX(safmin,anorm);
bscale = 1.f / MAX(safmin,bnorm);
/* Set Eigenvalues IHI+1:N */
i__1 = *n;
for (j = *ihi + 1; j <= i__1; ++j) {
absb = c_abs(&t[j + j * t_dim1]);
if (absb > safmin) {
i__2 = j + j * t_dim1;
q__2.r = t[i__2].r / absb, q__2.i = t[i__2].i / absb;
r_cnjg(&q__1, &q__2);
signbc.r = q__1.r, signbc.i = q__1.i;
i__2 = j + j * t_dim1;
t[i__2].r = absb, t[i__2].i = 0.f;
if (ilschr) {
i__2 = j - 1;
cscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1);
cscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1);
} else {
i__2 = j + j * h_dim1;
i__3 = j + j * h_dim1;
q__1.r = h__[i__3].r * signbc.r - h__[i__3].i * signbc.i,
q__1.i = h__[i__3].r * signbc.i + h__[i__3].i *
signbc.r;
h__[i__2].r = q__1.r, h__[i__2].i = q__1.i;
}
if (ilz) {
cscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1);
}
} else {
i__2 = j + j * t_dim1;
t[i__2].r = 0.f, t[i__2].i = 0.f;
}
i__2 = j;
i__3 = j + j * h_dim1;
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
i__2 = j;
i__3 = j + j * t_dim1;
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
/* L10: */
}
/* If IHI < ILO, skip QZ steps */
if (*ihi < *ilo) {
goto L190;
}
/* MAIN QZ ITERATION LOOP */
/* Initialize dynamic indices */
/* Eigenvalues ILAST+1:N have been found. */
/* Column operations modify rows IFRSTM:whatever */
/* Row operations modify columns whatever:ILASTM */
/* If only eigenvalues are being computed, then */
/* IFRSTM is the row of the last splitting row above row ILAST; */
/* this is always at least ILO. */
/* IITER counts iterations since the last eigenvalue was found, */
/* to tell when to use an extraordinary shift. */
/* MAXIT is the maximum number of QZ sweeps allowed. */
ilast = *ihi;
if (ilschr) {
ifrstm = 1;
ilastm = *n;
} else {
ifrstm = *ilo;
ilastm = *ihi;
}
iiter = 0;
eshift.r = 0.f, eshift.i = 0.f;
maxit = (*ihi - *ilo + 1) * 30;
i__1 = maxit;
for (jiter = 1; jiter <= i__1; ++jiter) {
/* Check for too many iterations. */
if (jiter > maxit) {
goto L180;
}
/* Split the matrix if possible. */
/* Two tests: */
/* 1: H(j,j-1)=0 or j=ILO */
/* 2: T(j,j)=0 */
/* Special case: j=ILAST */
if (ilast == *ilo) {
goto L60;
} else {
i__2 = ilast + (ilast - 1) * h_dim1;
if ((r__1 = h__[i__2].r, ABS(r__1)) + (r__2 = r_imag(&h__[ilast
+ (ilast - 1) * h_dim1]), ABS(r__2)) <= atol) {
i__2 = ilast + (ilast - 1) * h_dim1;
h__[i__2].r = 0.f, h__[i__2].i = 0.f;
goto L60;
}
}
if (c_abs(&t[ilast + ilast * t_dim1]) <= btol) {
i__2 = ilast + ilast * t_dim1;
t[i__2].r = 0.f, t[i__2].i = 0.f;
goto L50;
}
/* General case: j<ILAST */
i__2 = *ilo;
for (j = ilast - 1; j >= i__2; --j) {
/* Test 1: for H(j,j-1)=0 or j=ILO */
if (j == *ilo) {
ilazro = TRUE;
} else {
i__3 = j + (j - 1) * h_dim1;
if ((r__1 = h__[i__3].r, ABS(r__1)) + (r__2 = r_imag(&h__[j
+ (j - 1) * h_dim1]), ABS(r__2)) <= atol) {
i__3 = j + (j - 1) * h_dim1;
h__[i__3].r = 0.f, h__[i__3].i = 0.f;
ilazro = TRUE;
} else {
ilazro = FALSE;
}
}
/* Test 2: for T(j,j)=0 */
if (c_abs(&t[j + j * t_dim1]) < btol) {
i__3 = j + j * t_dim1;
t[i__3].r = 0.f, t[i__3].i = 0.f;
/* Test 1a: Check for 2 consecutive small subdiagonals in A */
ilazr2 = FALSE;
if (! ilazro) {
i__3 = j + (j - 1) * h_dim1;
i__4 = j + 1 + j * h_dim1;
i__5 = j + j * h_dim1;
if (((r__1 = h__[i__3].r, ABS(r__1)) + (r__2 = r_imag(&
h__[j + (j - 1) * h_dim1]), ABS(r__2))) * (
ascale * ((r__3 = h__[i__4].r, ABS(r__3)) + (
r__4 = r_imag(&h__[j + 1 + j * h_dim1]), ABS(
r__4)))) <= ((r__5 = h__[i__5].r, ABS(r__5)) + (
r__6 = r_imag(&h__[j + j * h_dim1]), ABS(r__6)))
* (ascale * atol)) {
ilazr2 = TRUE;
}
}
/* If both tests pass (1 & 2), i.e., the leading diagonal */
/* element of B in the block is zero, split a 1x1 block off */
/* at the top. (I.e., at the J-th row/column) The leading */
/* diagonal element of the remainder can also be zero, so */
/* this may have to be done repeatedly. */
if (ilazro || ilazr2) {
i__3 = ilast - 1;
for (jch = j; jch <= i__3; ++jch) {
i__4 = jch + jch * h_dim1;
ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i;
clartg_(&ctemp, &h__[jch + 1 + jch * h_dim1], &c__, &
s, &h__[jch + jch * h_dim1]);
i__4 = jch + 1 + jch * h_dim1;
h__[i__4].r = 0.f, h__[i__4].i = 0.f;
i__4 = ilastm - jch;
crot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, &
h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__,
&s);
i__4 = ilastm - jch;
crot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[
jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s);
if (ilq) {
r_cnjg(&q__1, &s);
crot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
* q_dim1 + 1], &c__1, &c__, &q__1);
}
if (ilazr2) {
i__4 = jch + (jch - 1) * h_dim1;
i__5 = jch + (jch - 1) * h_dim1;
q__1.r = c__ * h__[i__5].r, q__1.i = c__ * h__[
i__5].i;
h__[i__4].r = q__1.r, h__[i__4].i = q__1.i;
}
ilazr2 = FALSE;
i__4 = jch + 1 + (jch + 1) * t_dim1;
if ((r__1 = t[i__4].r, ABS(r__1)) + (r__2 = r_imag(&
t[jch + 1 + (jch + 1) * t_dim1]), ABS(r__2))
>= btol) {
if (jch + 1 >= ilast) {
goto L60;
} else {
ifirst = jch + 1;
goto L70;
}
}
i__4 = jch + 1 + (jch + 1) * t_dim1;
t[i__4].r = 0.f, t[i__4].i = 0.f;
/* L20: */
}
goto L50;
} else {
/* Only test 2 passed -- chase the zero to T(ILAST,ILAST) */
/* Then process as in the case T(ILAST,ILAST)=0 */
i__3 = ilast - 1;
for (jch = j; jch <= i__3; ++jch) {
i__4 = jch + (jch + 1) * t_dim1;
ctemp.r = t[i__4].r, ctemp.i = t[i__4].i;
clartg_(&ctemp, &t[jch + 1 + (jch + 1) * t_dim1], &
c__, &s, &t[jch + (jch + 1) * t_dim1]);
i__4 = jch + 1 + (jch + 1) * t_dim1;
t[i__4].r = 0.f, t[i__4].i = 0.f;
if (jch < ilastm - 1) {
i__4 = ilastm - jch - 1;
crot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, &
t[jch + 1 + (jch + 2) * t_dim1], ldt, &
c__, &s);
}
i__4 = ilastm - jch + 2;
crot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, &
h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__,
&s);
if (ilq) {
r_cnjg(&q__1, &s);
crot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
* q_dim1 + 1], &c__1, &c__, &q__1);
}
i__4 = jch + 1 + jch * h_dim1;
ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i;
clartg_(&ctemp, &h__[jch + 1 + (jch - 1) * h_dim1], &
c__, &s, &h__[jch + 1 + jch * h_dim1]);
i__4 = jch + 1 + (jch - 1) * h_dim1;
h__[i__4].r = 0.f, h__[i__4].i = 0.f;
i__4 = jch + 1 - ifrstm;
crot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[
ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s)
;
i__4 = jch - ifrstm;
crot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[
ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s)
;
if (ilz) {
crot_(n, &z__[jch * z_dim1 + 1], &c__1, &z__[(jch
- 1) * z_dim1 + 1], &c__1, &c__, &s);
}
/* L30: */
}
goto L50;
}
} else if (ilazro) {
/* Only test 1 passed -- work on J:ILAST */
ifirst = j;
goto L70;
}
/* Neither test passed -- try next J */
/* L40: */
}
/* (Drop-through is "impossible") */
*info = (*n << 1) + 1;
goto L210;
/* T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a */
/* 1x1 block. */
L50:
i__2 = ilast + ilast * h_dim1;
ctemp.r = h__[i__2].r, ctemp.i = h__[i__2].i;
clartg_(&ctemp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[
ilast + ilast * h_dim1]);
i__2 = ilast + (ilast - 1) * h_dim1;
h__[i__2].r = 0.f, h__[i__2].i = 0.f;
i__2 = ilast - ifrstm;
crot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + (
ilast - 1) * h_dim1], &c__1, &c__, &s);
i__2 = ilast - ifrstm;
crot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast -
1) * t_dim1], &c__1, &c__, &s);
if (ilz) {
crot_(n, &z__[ilast * z_dim1 + 1], &c__1, &z__[(ilast - 1) *
z_dim1 + 1], &c__1, &c__, &s);
}
/* H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHA and BETA */
L60:
absb = c_abs(&t[ilast + ilast * t_dim1]);
if (absb > safmin) {
i__2 = ilast + ilast * t_dim1;
q__2.r = t[i__2].r / absb, q__2.i = t[i__2].i / absb;
r_cnjg(&q__1, &q__2);
signbc.r = q__1.r, signbc.i = q__1.i;
i__2 = ilast + ilast * t_dim1;
t[i__2].r = absb, t[i__2].i = 0.f;
if (ilschr) {
i__2 = ilast - ifrstm;
cscal_(&i__2, &signbc, &t[ifrstm + ilast * t_dim1], &c__1);
i__2 = ilast + 1 - ifrstm;
cscal_(&i__2, &signbc, &h__[ifrstm + ilast * h_dim1], &c__1);
} else {
i__2 = ilast + ilast * h_dim1;
i__3 = ilast + ilast * h_dim1;
q__1.r = h__[i__3].r * signbc.r - h__[i__3].i * signbc.i,
q__1.i = h__[i__3].r * signbc.i + h__[i__3].i *
signbc.r;
h__[i__2].r = q__1.r, h__[i__2].i = q__1.i;
}
if (ilz) {
cscal_(n, &signbc, &z__[ilast * z_dim1 + 1], &c__1);
}
} else {
i__2 = ilast + ilast * t_dim1;
t[i__2].r = 0.f, t[i__2].i = 0.f;
}
i__2 = ilast;
i__3 = ilast + ilast * h_dim1;
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
i__2 = ilast;
i__3 = ilast + ilast * t_dim1;
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
/* Go to next block -- exit if finished. */
--ilast;
if (ilast < *ilo) {
goto L190;
}
/* Reset counters */
iiter = 0;
eshift.r = 0.f, eshift.i = 0.f;
if (! ilschr) {
ilastm = ilast;
if (ifrstm > ilast) {
ifrstm = *ilo;
}
}
goto L160;
/* QZ step */
/* This iteration only involves rows/columns IFIRST:ILAST. We */
/* assume IFIRST < ILAST, and that the diagonal of B is non-zero. */
L70:
++iiter;
if (! ilschr) {
ifrstm = ifirst;
}
/* Compute the Shift. */
/* At this point, IFIRST < ILAST, and the diagonal elements of */
/* T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in */
/* magnitude) */
if (iiter / 10 * 10 != iiter) {
/* The Wilkinson shift (AEP p.512), i.e., the eigenvalue of */
/* the bottom-right 2x2 block of A inv(B) which is nearest to */
/* the bottom-right element. */
/* We factor B as U*D, where U has unit diagonals, and */
/* compute (A*inv(D))*inv(U). */
i__2 = ilast - 1 + ilast * t_dim1;
q__2.r = bscale * t[i__2].r, q__2.i = bscale * t[i__2].i;
i__3 = ilast + ilast * t_dim1;
q__3.r = bscale * t[i__3].r, q__3.i = bscale * t[i__3].i;
c_div(&q__1, &q__2, &q__3);
u12.r = q__1.r, u12.i = q__1.i;
i__2 = ilast - 1 + (ilast - 1) * h_dim1;
q__2.r = ascale * h__[i__2].r, q__2.i = ascale * h__[i__2].i;
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
q__3.r = bscale * t[i__3].r, q__3.i = bscale * t[i__3].i;
c_div(&q__1, &q__2, &q__3);
ad11.r = q__1.r, ad11.i = q__1.i;
i__2 = ilast + (ilast - 1) * h_dim1;
q__2.r = ascale * h__[i__2].r, q__2.i = ascale * h__[i__2].i;
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
q__3.r = bscale * t[i__3].r, q__3.i = bscale * t[i__3].i;
c_div(&q__1, &q__2, &q__3);
ad21.r = q__1.r, ad21.i = q__1.i;
i__2 = ilast - 1 + ilast * h_dim1;
q__2.r = ascale * h__[i__2].r, q__2.i = ascale * h__[i__2].i;
i__3 = ilast + ilast * t_dim1;
q__3.r = bscale * t[i__3].r, q__3.i = bscale * t[i__3].i;
c_div(&q__1, &q__2, &q__3);
ad12.r = q__1.r, ad12.i = q__1.i;
i__2 = ilast + ilast * h_dim1;
q__2.r = ascale * h__[i__2].r, q__2.i = ascale * h__[i__2].i;
i__3 = ilast + ilast * t_dim1;
q__3.r = bscale * t[i__3].r, q__3.i = bscale * t[i__3].i;
c_div(&q__1, &q__2, &q__3);
ad22.r = q__1.r, ad22.i = q__1.i;
q__2.r = u12.r * ad21.r - u12.i * ad21.i, q__2.i = u12.r * ad21.i
+ u12.i * ad21.r;
q__1.r = ad22.r - q__2.r, q__1.i = ad22.i - q__2.i;
abi22.r = q__1.r, abi22.i = q__1.i;
q__2.r = ad11.r + abi22.r, q__2.i = ad11.i + abi22.i;
q__1.r = q__2.r * .5f, q__1.i = q__2.i * .5f;
t1.r = q__1.r, t1.i = q__1.i;
pow_ci(&q__4, &t1, &c__2);
q__5.r = ad12.r * ad21.r - ad12.i * ad21.i, q__5.i = ad12.r *
ad21.i + ad12.i * ad21.r;
q__3.r = q__4.r + q__5.r, q__3.i = q__4.i + q__5.i;
q__6.r = ad11.r * ad22.r - ad11.i * ad22.i, q__6.i = ad11.r *
ad22.i + ad11.i * ad22.r;
q__2.r = q__3.r - q__6.r, q__2.i = q__3.i - q__6.i;
c_sqrt(&q__1, &q__2);
rtdisc.r = q__1.r, rtdisc.i = q__1.i;
q__1.r = t1.r - abi22.r, q__1.i = t1.i - abi22.i;
q__2.r = t1.r - abi22.r, q__2.i = t1.i - abi22.i;
temp = q__1.r * rtdisc.r + r_imag(&q__2) * r_imag(&rtdisc);
if (temp <= 0.f) {
q__1.r = t1.r + rtdisc.r, q__1.i = t1.i + rtdisc.i;
shift.r = q__1.r, shift.i = q__1.i;
} else {
q__1.r = t1.r - rtdisc.r, q__1.i = t1.i - rtdisc.i;
shift.r = q__1.r, shift.i = q__1.i;
}
} else {
/* Exceptional shift. Chosen for no particularly good reason. */
i__2 = ilast - 1 + ilast * h_dim1;
q__4.r = ascale * h__[i__2].r, q__4.i = ascale * h__[i__2].i;
i__3 = ilast - 1 + (ilast - 1) * t_dim1;
q__5.r = bscale * t[i__3].r, q__5.i = bscale * t[i__3].i;
c_div(&q__3, &q__4, &q__5);
r_cnjg(&q__2, &q__3);
q__1.r = eshift.r + q__2.r, q__1.i = eshift.i + q__2.i;
eshift.r = q__1.r, eshift.i = q__1.i;
shift.r = eshift.r, shift.i = eshift.i;
}
/* Now check for two consecutive small subdiagonals. */
i__2 = ifirst + 1;
for (j = ilast - 1; j >= i__2; --j) {
istart = j;
i__3 = j + j * h_dim1;
q__2.r = ascale * h__[i__3].r, q__2.i = ascale * h__[i__3].i;
i__4 = j + j * t_dim1;
q__4.r = bscale * t[i__4].r, q__4.i = bscale * t[i__4].i;
q__3.r = shift.r * q__4.r - shift.i * q__4.i, q__3.i = shift.r *
q__4.i + shift.i * q__4.r;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
temp = (r__1 = ctemp.r, ABS(r__1)) + (r__2 = r_imag(&ctemp),
ABS(r__2));
i__3 = j + 1 + j * h_dim1;
temp2 = ascale * ((r__1 = h__[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&h__[j + 1 + j * h_dim1]), ABS(r__2)));
tempr = MAX(temp,temp2);
if (tempr < 1.f && tempr != 0.f) {
temp /= tempr;
temp2 /= tempr;
}
i__3 = j + (j - 1) * h_dim1;
if (((r__1 = h__[i__3].r, ABS(r__1)) + (r__2 = r_imag(&h__[j + (
j - 1) * h_dim1]), ABS(r__2))) * temp2 <= temp * atol) {
goto L90;
}
/* L80: */
}
istart = ifirst;
i__2 = ifirst + ifirst * h_dim1;
q__2.r = ascale * h__[i__2].r, q__2.i = ascale * h__[i__2].i;
i__3 = ifirst + ifirst * t_dim1;
q__4.r = bscale * t[i__3].r, q__4.i = bscale * t[i__3].i;
q__3.r = shift.r * q__4.r - shift.i * q__4.i, q__3.i = shift.r *
q__4.i + shift.i * q__4.r;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
L90:
/* Do an implicit-shift QZ sweep. */
/* Initial Q */
i__2 = istart + 1 + istart * h_dim1;
q__1.r = ascale * h__[i__2].r, q__1.i = ascale * h__[i__2].i;
ctemp2.r = q__1.r, ctemp2.i = q__1.i;
clartg_(&ctemp, &ctemp2, &c__, &s, &ctemp3);
/* Sweep */
i__2 = ilast - 1;
for (j = istart; j <= i__2; ++j) {
if (j > istart) {
i__3 = j + (j - 1) * h_dim1;
ctemp.r = h__[i__3].r, ctemp.i = h__[i__3].i;
clartg_(&ctemp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &
h__[j + (j - 1) * h_dim1]);
i__3 = j + 1 + (j - 1) * h_dim1;
h__[i__3].r = 0.f, h__[i__3].i = 0.f;
}
i__3 = ilastm;
for (jc = j; jc <= i__3; ++jc) {
i__4 = j + jc * h_dim1;
q__2.r = c__ * h__[i__4].r, q__2.i = c__ * h__[i__4].i;
i__5 = j + 1 + jc * h_dim1;
q__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, q__3.i = s.r *
h__[i__5].i + s.i * h__[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__4 = j + 1 + jc * h_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = j + jc * h_dim1;
q__2.r = q__3.r * h__[i__5].r - q__3.i * h__[i__5].i, q__2.i =
q__3.r * h__[i__5].i + q__3.i * h__[i__5].r;
i__6 = j + 1 + jc * h_dim1;
q__5.r = c__ * h__[i__6].r, q__5.i = c__ * h__[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
h__[i__4].r = q__1.r, h__[i__4].i = q__1.i;
i__4 = j + jc * h_dim1;
h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i;
i__4 = j + jc * t_dim1;
q__2.r = c__ * t[i__4].r, q__2.i = c__ * t[i__4].i;
i__5 = j + 1 + jc * t_dim1;
q__3.r = s.r * t[i__5].r - s.i * t[i__5].i, q__3.i = s.r * t[
i__5].i + s.i * t[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp2.r = q__1.r, ctemp2.i = q__1.i;
i__4 = j + 1 + jc * t_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = j + jc * t_dim1;
q__2.r = q__3.r * t[i__5].r - q__3.i * t[i__5].i, q__2.i =
q__3.r * t[i__5].i + q__3.i * t[i__5].r;
i__6 = j + 1 + jc * t_dim1;
q__5.r = c__ * t[i__6].r, q__5.i = c__ * t[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
t[i__4].r = q__1.r, t[i__4].i = q__1.i;
i__4 = j + jc * t_dim1;
t[i__4].r = ctemp2.r, t[i__4].i = ctemp2.i;
/* L100: */
}
if (ilq) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
i__4 = jr + j * q_dim1;
q__2.r = c__ * q[i__4].r, q__2.i = c__ * q[i__4].i;
r_cnjg(&q__4, &s);
i__5 = jr + (j + 1) * q_dim1;
q__3.r = q__4.r * q[i__5].r - q__4.i * q[i__5].i, q__3.i =
q__4.r * q[i__5].i + q__4.i * q[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__4 = jr + (j + 1) * q_dim1;
q__3.r = -s.r, q__3.i = -s.i;
i__5 = jr + j * q_dim1;
q__2.r = q__3.r * q[i__5].r - q__3.i * q[i__5].i, q__2.i =
q__3.r * q[i__5].i + q__3.i * q[i__5].r;
i__6 = jr + (j + 1) * q_dim1;
q__4.r = c__ * q[i__6].r, q__4.i = c__ * q[i__6].i;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
q[i__4].r = q__1.r, q[i__4].i = q__1.i;
i__4 = jr + j * q_dim1;
q[i__4].r = ctemp.r, q[i__4].i = ctemp.i;
/* L110: */
}
}
i__3 = j + 1 + (j + 1) * t_dim1;
ctemp.r = t[i__3].r, ctemp.i = t[i__3].i;
clartg_(&ctemp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j +
1) * t_dim1]);
i__3 = j + 1 + j * t_dim1;
t[i__3].r = 0.f, t[i__3].i = 0.f;
/* Computing MIN */
i__4 = j + 2;
i__3 = MIN(i__4,ilast);
for (jr = ifrstm; jr <= i__3; ++jr) {
i__4 = jr + (j + 1) * h_dim1;
q__2.r = c__ * h__[i__4].r, q__2.i = c__ * h__[i__4].i;
i__5 = jr + j * h_dim1;
q__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, q__3.i = s.r *
h__[i__5].i + s.i * h__[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__4 = jr + j * h_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = jr + (j + 1) * h_dim1;
q__2.r = q__3.r * h__[i__5].r - q__3.i * h__[i__5].i, q__2.i =
q__3.r * h__[i__5].i + q__3.i * h__[i__5].r;
i__6 = jr + j * h_dim1;
q__5.r = c__ * h__[i__6].r, q__5.i = c__ * h__[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
h__[i__4].r = q__1.r, h__[i__4].i = q__1.i;
i__4 = jr + (j + 1) * h_dim1;
h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i;
/* L120: */
}
i__3 = j;
for (jr = ifrstm; jr <= i__3; ++jr) {
i__4 = jr + (j + 1) * t_dim1;
q__2.r = c__ * t[i__4].r, q__2.i = c__ * t[i__4].i;
i__5 = jr + j * t_dim1;
q__3.r = s.r * t[i__5].r - s.i * t[i__5].i, q__3.i = s.r * t[
i__5].i + s.i * t[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__4 = jr + j * t_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = jr + (j + 1) * t_dim1;
q__2.r = q__3.r * t[i__5].r - q__3.i * t[i__5].i, q__2.i =
q__3.r * t[i__5].i + q__3.i * t[i__5].r;
i__6 = jr + j * t_dim1;
q__5.r = c__ * t[i__6].r, q__5.i = c__ * t[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
t[i__4].r = q__1.r, t[i__4].i = q__1.i;
i__4 = jr + (j + 1) * t_dim1;
t[i__4].r = ctemp.r, t[i__4].i = ctemp.i;
/* L130: */
}
if (ilz) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
i__4 = jr + (j + 1) * z_dim1;
q__2.r = c__ * z__[i__4].r, q__2.i = c__ * z__[i__4].i;
i__5 = jr + j * z_dim1;
q__3.r = s.r * z__[i__5].r - s.i * z__[i__5].i, q__3.i =
s.r * z__[i__5].i + s.i * z__[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__4 = jr + j * z_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = jr + (j + 1) * z_dim1;
q__2.r = q__3.r * z__[i__5].r - q__3.i * z__[i__5].i,
q__2.i = q__3.r * z__[i__5].i + q__3.i * z__[i__5]
.r;
i__6 = jr + j * z_dim1;
q__5.r = c__ * z__[i__6].r, q__5.i = c__ * z__[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
z__[i__4].r = q__1.r, z__[i__4].i = q__1.i;
i__4 = jr + (j + 1) * z_dim1;
z__[i__4].r = ctemp.r, z__[i__4].i = ctemp.i;
/* L140: */
}
}
/* L150: */
}
L160:
/* L170: */
;
}
/* Drop-through = non-convergence */
L180:
*info = ilast;
goto L210;
/* Successful completion of all QZ steps */
L190:
/* Set Eigenvalues 1:ILO-1 */
i__1 = *ilo - 1;
for (j = 1; j <= i__1; ++j) {
absb = c_abs(&t[j + j * t_dim1]);
if (absb > safmin) {
i__2 = j + j * t_dim1;
q__2.r = t[i__2].r / absb, q__2.i = t[i__2].i / absb;
r_cnjg(&q__1, &q__2);
signbc.r = q__1.r, signbc.i = q__1.i;
i__2 = j + j * t_dim1;
t[i__2].r = absb, t[i__2].i = 0.f;
if (ilschr) {
i__2 = j - 1;
cscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1);
cscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1);
} else {
i__2 = j + j * h_dim1;
i__3 = j + j * h_dim1;
q__1.r = h__[i__3].r * signbc.r - h__[i__3].i * signbc.i,
q__1.i = h__[i__3].r * signbc.i + h__[i__3].i *
signbc.r;
h__[i__2].r = q__1.r, h__[i__2].i = q__1.i;
}
if (ilz) {
cscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1);
}
} else {
i__2 = j + j * t_dim1;
t[i__2].r = 0.f, t[i__2].i = 0.f;
}
i__2 = j;
i__3 = j + j * h_dim1;
alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i;
i__2 = j;
i__3 = j + j * t_dim1;
beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i;
/* L200: */
}
/* Normal Termination */
*info = 0;
/* Exit (other than argument error) -- return optimal workspace size */
L210:
q__1.r = (float) (*n), q__1.i = 0.f;
work[1].r = q__1.r, work[1].i = q__1.i;
return 0;
/* End of CHGEQZ */
} /* chgeqz_ */
real scasum_(integer *n, complex *cx, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
real ret_val, r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, nincx;
real stemp;
/* takes the sum of the absolute values of a complex vector and */
/* returns a single precision result. */
/* jack dongarra, linpack, 3/11/78. */
/* modified 3/93 to return if incx .le. 0. */
/* modified 12/3/93, array(1) declarations changed to array(*) */
/* Parameter adjustments */
--cx;
/* Function Body */
ret_val = 0.f;
stemp = 0.f;
if (*n <= 0 || *incx <= 0) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
i__3 = i__;
stemp = stemp + (r__1 = cx[i__3].r, abs(r__1)) + (r__2 = r_imag(&cx[
i__]), abs(r__2));
/* L10: */
}
ret_val = stemp;
return ret_val;
/* code for increment equal to 1 */
L20:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = i__;
stemp = stemp + (r__1 = cx[i__1].r, abs(r__1)) + (r__2 = r_imag(&cx[
i__]), abs(r__2));
/* L30: */
}
ret_val = stemp;
return ret_val;
} /* scasum_ */
/*< subroutine csvdc(x,ldx,n,p,s,e,u,ldu,v,ldv,work,job,info) >*/
/* Subroutine */ int csvdc_(complex *x, integer *ldx, integer *n, integer *p,
complex *s, complex *e, complex *u, integer *ldu, complex *v, integer
*ldv, complex *work, integer *job, integer *info)
{
/* System generated locals */
integer x_dim1, x_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2,
i__3, i__4;
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3;
/* Builtin functions */
double r_imag(complex *), c_abs(complex *);
void c_div(complex *, complex *, complex *), r_cnjg(complex *, complex *);
double sqrt(doublereal);
/* Local variables */
real b, c__, f, g;
integer i__, j, k, l=0, m;
complex r__, t;
real t1, el;
integer kk;
real cs;
integer ll, mm, ls=0;
real sl;
integer lu;
real sm, sn;
integer lm1, mm1, lp1, mp1, nct, ncu, lls, nrt;
real emm1, smm1;
integer kase, jobu, iter;
real test;
integer nctp1, nrtp1;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
real scale;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
real shift;
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *);
integer maxit;
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), csrot_(integer *, complex *,
integer *, complex *, integer *, real *, real *);
logical wantu, wantv;
extern /* Subroutine */ int srotg_(real *, real *, real *, real *);
real ztest;
extern doublereal scnrm2_(integer *, complex *, integer *);
/*< integer ldx,n,p,ldu,ldv,job,info >*/
/*< complex x(ldx,1),s(1),e(1),u(ldu,1),v(ldv,1),work(1) >*/
/* csvdc is a subroutine to reduce a complex nxp matrix x by */
/* unitary transformations u and v to diagonal form. the */
/* diagonal elements s(i) are the singular values of x. the */
/* columns of u are the corresponding left singular vectors, */
/* and the columns of v the right singular vectors. */
/* on entry */
/* x complex(ldx,p), where ldx.ge.n. */
/* x contains the matrix whose singular value */
/* decomposition is to be computed. x is */
/* destroyed by csvdc. */
/* ldx integer. */
/* ldx is the leading dimension of the array x. */
/* n integer. */
/* n is the number of rows of the matrix x. */
/* p integer. */
/* p is the number of columns of the matrix x. */
/* ldu integer. */
/* ldu is the leading dimension of the array u */
/* (see below). */
/* ldv integer. */
/* ldv is the leading dimension of the array v */
/* (see below). */
/* work complex(n). */
/* work is a scratch array. */
/* job integer. */
/* job controls the computation of the singular */
/* vectors. it has the decimal expansion ab */
/* with the following meaning */
/* a.eq.0 do not compute the left singular */
/* vectors. */
/* a.eq.1 return the n left singular vectors */
/* in u. */
/* a.ge.2 returns the first min(n,p) */
/* left singular vectors in u. */
/* b.eq.0 do not compute the right singular */
/* vectors. */
/* b.eq.1 return the right singular vectors */
/* in v. */
/* on return */
/* s complex(mm), where mm=min(n+1,p). */
/* the first min(n,p) entries of s contain the */
/* singular values of x arranged in descending */
/* order of magnitude. */
/* e complex(p). */
/* e ordinarily contains zeros. however see the */
/* discussion of info for exceptions. */
/* u complex(ldu,k), where ldu.ge.n. if joba.eq.1 then */
/* k.eq.n, if joba.ge.2 then */
/* k.eq.min(n,p). */
/* u contains the matrix of left singular vectors. */
/* u is not referenced if joba.eq.0. if n.le.p */
/* or if joba.gt.2, then u may be identified with x */
/* in the subroutine call. */
/* v complex(ldv,p), where ldv.ge.p. */
/* v contains the matrix of right singular vectors. */
/* v is not referenced if jobb.eq.0. if p.le.n, */
/* then v may be identified whth x in the */
/* subroutine call. */
/* info integer. */
/* the singular values (and their corresponding */
/* singular vectors) s(info+1),s(info+2),...,s(m) */
/* are correct (here m=min(n,p)). thus if */
/* info.eq.0, all the singular values and their */
/* vectors are correct. in any event, the matrix */
/* b = ctrans(u)*x*v is the bidiagonal matrix */
/* with the elements of s on its diagonal and the */
/* elements of e on its super-diagonal (ctrans(u) */
/* is the conjugate-transpose of u). thus the */
/* singular values of x and b are the same. */
/* linpack. this version dated 03/19/79 . */
/* correction to shift calculation made 2/85. */
/* g.w. stewart, university of maryland, argonne national lab. */
/* csvdc uses the following functions and subprograms. */
/* external csrot */
/* blas caxpy,cdotc,cscal,cswap,scnrm2,srotg */
/* fortran abs,aimag,amax1,cabs,cmplx */
/* fortran conjg,max0,min0,mod,real,sqrt */
/* internal variables */
/*< >*/
/*< complex cdotc,t,r >*/
/*< >*/
/*< logical wantu,wantv >*/
/*< complex csign,zdum,zdum1,zdum2 >*/
/*< real cabs1 >*/
/*< cabs1(zdum) = abs(real(zdum)) + abs(aimag(zdum)) >*/
/*< csign(zdum1,zdum2) = cabs(zdum1)*(zdum2/cabs(zdum2)) >*/
/* set the maximum number of iterations. */
/*< maxit = 1000 >*/
/* Parameter adjustments */
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--s;
--e;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--work;
/* Function Body */
maxit = 1000;
/* determine what is to be computed. */
/*< wantu = .false. >*/
wantu = FALSE_;
/*< wantv = .false. >*/
wantv = FALSE_;
/*< jobu = mod(job,100)/10 >*/
jobu = *job % 100 / 10;
/*< ncu = n >*/
ncu = *n;
/*< if (jobu .gt. 1) ncu = min0(n,p) >*/
if (jobu > 1) {
ncu = min(*n,*p);
}
/*< if (jobu .ne. 0) wantu = .true. >*/
if (jobu != 0) {
wantu = TRUE_;
}
/*< if (mod(job,10) .ne. 0) wantv = .true. >*/
if (*job % 10 != 0) {
wantv = TRUE_;
}
/* reduce x to bidiagonal form, storing the diagonal elements */
/* in s and the super-diagonal elements in e. */
/*< info = 0 >*/
*info = 0;
/*< nct = min0(n-1,p) >*/
/* Computing MIN */
i__1 = *n - 1;
nct = min(i__1,*p);
/*< nrt = max0(0,min0(p-2,n)) >*/
/* Computing MAX */
/* Computing MIN */
i__3 = *p - 2;
i__1 = 0, i__2 = min(i__3,*n);
nrt = max(i__1,i__2);
/*< lu = max0(nct,nrt) >*/
lu = max(nct,nrt);
/*< if (lu .lt. 1) go to 170 >*/
if (lu < 1) {
goto L170;
}
/*< do 160 l = 1, lu >*/
i__1 = lu;
for (l = 1; l <= i__1; ++l) {
/*< lp1 = l + 1 >*/
lp1 = l + 1;
/*< if (l .gt. nct) go to 20 >*/
if (l > nct) {
goto L20;
}
/* compute the transformation for the l-th column and */
/* place the l-th diagonal in s(l). */
/*< s(l) = cmplx(scnrm2(n-l+1,x(l,l),1),0.0e0) >*/
i__2 = l;
i__3 = *n - l + 1;
r__1 = scnrm2_(&i__3, &x[l + l * x_dim1], &c__1);
q__1.r = r__1, q__1.i = (float)0.;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< if (cabs1(s(l)) .eq. 0.0e0) go to 10 >*/
i__2 = l;
if ((r__1 = s[i__2].r, dabs(r__1)) + (r__2 = r_imag(&s[l]), dabs(r__2)
) == (float)0.) {
goto L10;
}
/*< if (cabs1(x(l,l)) .ne. 0.0e0) s(l) = csign(s(l),x(l,l)) >*/
i__2 = l + l * x_dim1;
if ((r__1 = x[i__2].r, dabs(r__1)) + (r__2 = r_imag(&x[l + l * x_dim1]
), dabs(r__2)) != (float)0.) {
i__3 = l;
r__3 = c_abs(&s[l]);
i__4 = l + l * x_dim1;
r__4 = c_abs(&x[l + l * x_dim1]);
q__2.r = x[i__4].r / r__4, q__2.i = x[i__4].i / r__4;
q__1.r = r__3 * q__2.r, q__1.i = r__3 * q__2.i;
s[i__3].r = q__1.r, s[i__3].i = q__1.i;
}
/*< call cscal(n-l+1,1.0e0/s(l),x(l,l),1) >*/
i__2 = *n - l + 1;
c_div(&q__1, &c_b8, &s[l]);
cscal_(&i__2, &q__1, &x[l + l * x_dim1], &c__1);
/*< x(l,l) = (1.0e0,0.0e0) + x(l,l) >*/
i__2 = l + l * x_dim1;
i__3 = l + l * x_dim1;
q__1.r = x[i__3].r + (float)1., q__1.i = x[i__3].i + (float)0.;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
/*< 10 continue >*/
L10:
/*< s(l) = -s(l) >*/
i__2 = l;
i__3 = l;
q__1.r = -s[i__3].r, q__1.i = -s[i__3].i;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< 20 continue >*/
L20:
/*< if (p .lt. lp1) go to 50 >*/
if (*p < lp1) {
goto L50;
}
/*< do 40 j = lp1, p >*/
i__2 = *p;
for (j = lp1; j <= i__2; ++j) {
/*< if (l .gt. nct) go to 30 >*/
if (l > nct) {
goto L30;
}
/*< if (cabs1(s(l)) .eq. 0.0e0) go to 30 >*/
i__3 = l;
if ((r__1 = s[i__3].r, dabs(r__1)) + (r__2 = r_imag(&s[l]), dabs(
r__2)) == (float)0.) {
goto L30;
}
/* apply the transformation. */
/*< t = -cdotc(n-l+1,x(l,l),1,x(l,j),1)/x(l,l) >*/
i__3 = *n - l + 1;
cdotc_(&q__3, &i__3, &x[l + l * x_dim1], &c__1, &x[l + j * x_dim1]
, &c__1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
c_div(&q__1, &q__2, &x[l + l * x_dim1]);
t.r = q__1.r, t.i = q__1.i;
/*< call caxpy(n-l+1,t,x(l,l),1,x(l,j),1) >*/
i__3 = *n - l + 1;
caxpy_(&i__3, &t, &x[l + l * x_dim1], &c__1, &x[l + j * x_dim1], &
c__1);
/*< 30 continue >*/
L30:
/* place the l-th row of x into e for the */
/* subsequent calculation of the row transformation. */
/*< e(j) = conjg(x(l,j)) >*/
i__3 = j;
r_cnjg(&q__1, &x[l + j * x_dim1]);
e[i__3].r = q__1.r, e[i__3].i = q__1.i;
/*< 40 continue >*/
/* L40: */
}
/*< 50 continue >*/
L50:
/*< if (.not.wantu .or. l .gt. nct) go to 70 >*/
if (! wantu || l > nct) {
goto L70;
}
/* place the transformation in u for subsequent back */
/* multiplication. */
/*< do 60 i = l, n >*/
i__2 = *n;
for (i__ = l; i__ <= i__2; ++i__) {
/*< u(i,l) = x(i,l) >*/
i__3 = i__ + l * u_dim1;
i__4 = i__ + l * x_dim1;
u[i__3].r = x[i__4].r, u[i__3].i = x[i__4].i;
/*< 60 continue >*/
/* L60: */
}
/*< 70 continue >*/
L70:
/*< if (l .gt. nrt) go to 150 >*/
if (l > nrt) {
goto L150;
}
/* compute the l-th row transformation and place the */
/* l-th super-diagonal in e(l). */
/*< e(l) = cmplx(scnrm2(p-l,e(lp1),1),0.0e0) >*/
i__2 = l;
i__3 = *p - l;
r__1 = scnrm2_(&i__3, &e[lp1], &c__1);
q__1.r = r__1, q__1.i = (float)0.;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< if (cabs1(e(l)) .eq. 0.0e0) go to 80 >*/
i__2 = l;
if ((r__1 = e[i__2].r, dabs(r__1)) + (r__2 = r_imag(&e[l]), dabs(r__2)
) == (float)0.) {
goto L80;
}
/*< if (cabs1(e(lp1)) .ne. 0.0e0) e(l) = csign(e(l),e(lp1)) >*/
i__2 = lp1;
if ((r__1 = e[i__2].r, dabs(r__1)) + (r__2 = r_imag(&e[lp1]), dabs(
r__2)) != (float)0.) {
i__3 = l;
r__3 = c_abs(&e[l]);
i__4 = lp1;
r__4 = c_abs(&e[lp1]);
q__2.r = e[i__4].r / r__4, q__2.i = e[i__4].i / r__4;
q__1.r = r__3 * q__2.r, q__1.i = r__3 * q__2.i;
e[i__3].r = q__1.r, e[i__3].i = q__1.i;
}
/*< call cscal(p-l,1.0e0/e(l),e(lp1),1) >*/
i__2 = *p - l;
c_div(&q__1, &c_b8, &e[l]);
cscal_(&i__2, &q__1, &e[lp1], &c__1);
/*< e(lp1) = (1.0e0,0.0e0) + e(lp1) >*/
i__2 = lp1;
i__3 = lp1;
q__1.r = e[i__3].r + (float)1., q__1.i = e[i__3].i + (float)0.;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< 80 continue >*/
L80:
/*< e(l) = -conjg(e(l)) >*/
i__2 = l;
r_cnjg(&q__2, &e[l]);
q__1.r = -q__2.r, q__1.i = -q__2.i;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< if (lp1 .gt. n .or. cabs1(e(l)) .eq. 0.0e0) go to 120 >*/
i__2 = l;
if (lp1 > *n || (r__1 = e[i__2].r, dabs(r__1)) + (r__2 = r_imag(&e[l])
, dabs(r__2)) == (float)0.) {
goto L120;
}
/* apply the transformation. */
/*< do 90 i = lp1, n >*/
i__2 = *n;
for (i__ = lp1; i__ <= i__2; ++i__) {
/*< work(i) = (0.0e0,0.0e0) >*/
i__3 = i__;
work[i__3].r = (float)0., work[i__3].i = (float)0.;
/*< 90 continue >*/
/* L90: */
}
/*< do 100 j = lp1, p >*/
i__2 = *p;
for (j = lp1; j <= i__2; ++j) {
/*< call caxpy(n-l,e(j),x(lp1,j),1,work(lp1),1) >*/
i__3 = *n - l;
caxpy_(&i__3, &e[j], &x[lp1 + j * x_dim1], &c__1, &work[lp1], &
c__1);
/*< 100 continue >*/
/* L100: */
}
/*< do 110 j = lp1, p >*/
i__2 = *p;
for (j = lp1; j <= i__2; ++j) {
/*< >*/
i__3 = *n - l;
i__4 = j;
q__3.r = -e[i__4].r, q__3.i = -e[i__4].i;
c_div(&q__2, &q__3, &e[lp1]);
r_cnjg(&q__1, &q__2);
caxpy_(&i__3, &q__1, &work[lp1], &c__1, &x[lp1 + j * x_dim1], &
c__1);
/*< 110 continue >*/
/* L110: */
}
/*< 120 continue >*/
L120:
/*< if (.not.wantv) go to 140 >*/
if (! wantv) {
goto L140;
}
/* place the transformation in v for subsequent */
/* back multiplication. */
/*< do 130 i = lp1, p >*/
i__2 = *p;
for (i__ = lp1; i__ <= i__2; ++i__) {
/*< v(i,l) = e(i) >*/
i__3 = i__ + l * v_dim1;
i__4 = i__;
v[i__3].r = e[i__4].r, v[i__3].i = e[i__4].i;
/*< 130 continue >*/
/* L130: */
}
/*< 140 continue >*/
L140:
/*< 150 continue >*/
L150:
/*< 160 continue >*/
/* L160: */
;
}
/*< 170 continue >*/
L170:
/* set up the final bidiagonal matrix or order m. */
/*< m = min0(p,n+1) >*/
/* Computing MIN */
i__1 = *p, i__2 = *n + 1;
m = min(i__1,i__2);
/*< nctp1 = nct + 1 >*/
nctp1 = nct + 1;
/*< nrtp1 = nrt + 1 >*/
nrtp1 = nrt + 1;
/*< if (nct .lt. p) s(nctp1) = x(nctp1,nctp1) >*/
if (nct < *p) {
i__1 = nctp1;
i__2 = nctp1 + nctp1 * x_dim1;
s[i__1].r = x[i__2].r, s[i__1].i = x[i__2].i;
}
/*< if (n .lt. m) s(m) = (0.0e0,0.0e0) >*/
if (*n < m) {
i__1 = m;
s[i__1].r = (float)0., s[i__1].i = (float)0.;
}
/*< if (nrtp1 .lt. m) e(nrtp1) = x(nrtp1,m) >*/
if (nrtp1 < m) {
i__1 = nrtp1;
i__2 = nrtp1 + m * x_dim1;
e[i__1].r = x[i__2].r, e[i__1].i = x[i__2].i;
}
/*< e(m) = (0.0e0,0.0e0) >*/
i__1 = m;
e[i__1].r = (float)0., e[i__1].i = (float)0.;
/* if required, generate u. */
/*< if (.not.wantu) go to 300 >*/
if (! wantu) {
goto L300;
}
/*< if (ncu .lt. nctp1) go to 200 >*/
if (ncu < nctp1) {
goto L200;
}
/*< do 190 j = nctp1, ncu >*/
i__1 = ncu;
for (j = nctp1; j <= i__1; ++j) {
/*< do 180 i = 1, n >*/
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< u(i,j) = (0.0e0,0.0e0) >*/
i__3 = i__ + j * u_dim1;
u[i__3].r = (float)0., u[i__3].i = (float)0.;
/*< 180 continue >*/
/* L180: */
}
/*< u(j,j) = (1.0e0,0.0e0) >*/
i__2 = j + j * u_dim1;
u[i__2].r = (float)1., u[i__2].i = (float)0.;
/*< 190 continue >*/
/* L190: */
}
/*< 200 continue >*/
L200:
/*< if (nct .lt. 1) go to 290 >*/
if (nct < 1) {
goto L290;
}
/*< do 280 ll = 1, nct >*/
i__1 = nct;
for (ll = 1; ll <= i__1; ++ll) {
/*< l = nct - ll + 1 >*/
l = nct - ll + 1;
/*< if (cabs1(s(l)) .eq. 0.0e0) go to 250 >*/
i__2 = l;
if ((r__1 = s[i__2].r, dabs(r__1)) + (r__2 = r_imag(&s[l]), dabs(r__2)
) == (float)0.) {
goto L250;
}
/*< lp1 = l + 1 >*/
lp1 = l + 1;
/*< if (ncu .lt. lp1) go to 220 >*/
if (ncu < lp1) {
goto L220;
}
/*< do 210 j = lp1, ncu >*/
i__2 = ncu;
for (j = lp1; j <= i__2; ++j) {
/*< t = -cdotc(n-l+1,u(l,l),1,u(l,j),1)/u(l,l) >*/
i__3 = *n - l + 1;
cdotc_(&q__3, &i__3, &u[l + l * u_dim1], &c__1, &u[l + j * u_dim1]
, &c__1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
c_div(&q__1, &q__2, &u[l + l * u_dim1]);
t.r = q__1.r, t.i = q__1.i;
/*< call caxpy(n-l+1,t,u(l,l),1,u(l,j),1) >*/
i__3 = *n - l + 1;
caxpy_(&i__3, &t, &u[l + l * u_dim1], &c__1, &u[l + j * u_dim1], &
c__1);
/*< 210 continue >*/
/* L210: */
}
/*< 220 continue >*/
L220:
/*< call cscal(n-l+1,(-1.0e0,0.0e0),u(l,l),1) >*/
i__2 = *n - l + 1;
cscal_(&i__2, &c_b53, &u[l + l * u_dim1], &c__1);
/*< u(l,l) = (1.0e0,0.0e0) + u(l,l) >*/
i__2 = l + l * u_dim1;
i__3 = l + l * u_dim1;
q__1.r = u[i__3].r + (float)1., q__1.i = u[i__3].i + (float)0.;
u[i__2].r = q__1.r, u[i__2].i = q__1.i;
/*< lm1 = l - 1 >*/
lm1 = l - 1;
/*< if (lm1 .lt. 1) go to 240 >*/
if (lm1 < 1) {
goto L240;
}
/*< do 230 i = 1, lm1 >*/
i__2 = lm1;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< u(i,l) = (0.0e0,0.0e0) >*/
i__3 = i__ + l * u_dim1;
u[i__3].r = (float)0., u[i__3].i = (float)0.;
/*< 230 continue >*/
/* L230: */
}
/*< 240 continue >*/
L240:
/*< go to 270 >*/
goto L270;
/*< 250 continue >*/
L250:
/*< do 260 i = 1, n >*/
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< u(i,l) = (0.0e0,0.0e0) >*/
i__3 = i__ + l * u_dim1;
u[i__3].r = (float)0., u[i__3].i = (float)0.;
/*< 260 continue >*/
/* L260: */
}
/*< u(l,l) = (1.0e0,0.0e0) >*/
i__2 = l + l * u_dim1;
u[i__2].r = (float)1., u[i__2].i = (float)0.;
/*< 270 continue >*/
L270:
/*< 280 continue >*/
/* L280: */
;
}
/*< 290 continue >*/
L290:
/*< 300 continue >*/
L300:
/* if it is required, generate v. */
/*< if (.not.wantv) go to 350 >*/
if (! wantv) {
goto L350;
}
/*< do 340 ll = 1, p >*/
i__1 = *p;
for (ll = 1; ll <= i__1; ++ll) {
/*< l = p - ll + 1 >*/
l = *p - ll + 1;
/*< lp1 = l + 1 >*/
lp1 = l + 1;
/*< if (l .gt. nrt) go to 320 >*/
if (l > nrt) {
goto L320;
}
/*< if (cabs1(e(l)) .eq. 0.0e0) go to 320 >*/
i__2 = l;
if ((r__1 = e[i__2].r, dabs(r__1)) + (r__2 = r_imag(&e[l]), dabs(r__2)
) == (float)0.) {
goto L320;
}
/*< do 310 j = lp1, p >*/
i__2 = *p;
for (j = lp1; j <= i__2; ++j) {
/*< t = -cdotc(p-l,v(lp1,l),1,v(lp1,j),1)/v(lp1,l) >*/
i__3 = *p - l;
cdotc_(&q__3, &i__3, &v[lp1 + l * v_dim1], &c__1, &v[lp1 + j *
v_dim1], &c__1);
q__2.r = -q__3.r, q__2.i = -q__3.i;
c_div(&q__1, &q__2, &v[lp1 + l * v_dim1]);
t.r = q__1.r, t.i = q__1.i;
/*< call caxpy(p-l,t,v(lp1,l),1,v(lp1,j),1) >*/
i__3 = *p - l;
caxpy_(&i__3, &t, &v[lp1 + l * v_dim1], &c__1, &v[lp1 + j *
v_dim1], &c__1);
/*< 310 continue >*/
/* L310: */
}
/*< 320 continue >*/
L320:
/*< do 330 i = 1, p >*/
i__2 = *p;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< v(i,l) = (0.0e0,0.0e0) >*/
i__3 = i__ + l * v_dim1;
v[i__3].r = (float)0., v[i__3].i = (float)0.;
/*< 330 continue >*/
/* L330: */
}
/*< v(l,l) = (1.0e0,0.0e0) >*/
i__2 = l + l * v_dim1;
v[i__2].r = (float)1., v[i__2].i = (float)0.;
/*< 340 continue >*/
/* L340: */
}
/*< 350 continue >*/
L350:
/* transform s and e so that they are real. */
/*< do 380 i = 1, m >*/
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< if (cabs1(s(i)) .eq. 0.0e0) go to 360 >*/
i__2 = i__;
if ((r__1 = s[i__2].r, dabs(r__1)) + (r__2 = r_imag(&s[i__]), dabs(
r__2)) == (float)0.) {
goto L360;
}
/*< t = cmplx(cabs(s(i)),0.0e0) >*/
r__1 = c_abs(&s[i__]);
q__1.r = r__1, q__1.i = (float)0.;
t.r = q__1.r, t.i = q__1.i;
/*< r = s(i)/t >*/
c_div(&q__1, &s[i__], &t);
r__.r = q__1.r, r__.i = q__1.i;
/*< s(i) = t >*/
i__2 = i__;
s[i__2].r = t.r, s[i__2].i = t.i;
/*< if (i .lt. m) e(i) = e(i)/r >*/
if (i__ < m) {
i__2 = i__;
c_div(&q__1, &e[i__], &r__);
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
}
/*< if (wantu) call cscal(n,r,u(1,i),1) >*/
if (wantu) {
cscal_(n, &r__, &u[i__ * u_dim1 + 1], &c__1);
}
/*< 360 continue >*/
L360:
/* ...exit */
/*< if (i .eq. m) go to 390 >*/
if (i__ == m) {
goto L390;
}
/*< if (cabs1(e(i)) .eq. 0.0e0) go to 370 >*/
i__2 = i__;
if ((r__1 = e[i__2].r, dabs(r__1)) + (r__2 = r_imag(&e[i__]), dabs(
r__2)) == (float)0.) {
goto L370;
}
/*< t = cmplx(cabs(e(i)),0.0e0) >*/
r__1 = c_abs(&e[i__]);
q__1.r = r__1, q__1.i = (float)0.;
t.r = q__1.r, t.i = q__1.i;
/*< r = t/e(i) >*/
c_div(&q__1, &t, &e[i__]);
r__.r = q__1.r, r__.i = q__1.i;
/*< e(i) = t >*/
i__2 = i__;
e[i__2].r = t.r, e[i__2].i = t.i;
/*< s(i+1) = s(i+1)*r >*/
i__2 = i__ + 1;
i__3 = i__ + 1;
q__1.r = s[i__3].r * r__.r - s[i__3].i * r__.i, q__1.i = s[i__3].r *
r__.i + s[i__3].i * r__.r;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< if (wantv) call cscal(p,r,v(1,i+1),1) >*/
if (wantv) {
cscal_(p, &r__, &v[(i__ + 1) * v_dim1 + 1], &c__1);
}
/*< 370 continue >*/
L370:
/*< 380 continue >*/
/* L380: */
;
}
/*< 390 continue >*/
L390:
/* main iteration loop for the singular values. */
/*< mm = m >*/
mm = m;
/*< iter = 0 >*/
iter = 0;
/*< 400 continue >*/
L400:
/* quit if all the singular values have been found. */
/* ...exit */
/*< if (m .eq. 0) go to 660 >*/
if (m == 0) {
goto L660;
}
/* if too many iterations have been performed, set */
/* flag and return. */
/*< if (iter .lt. maxit) go to 410 >*/
if (iter < maxit) {
goto L410;
}
/*< info = m >*/
*info = m;
/* ......exit */
/*< go to 660 >*/
goto L660;
/*< 410 continue >*/
L410:
/* this section of the program inspects for */
/* negligible elements in the s and e arrays. on */
/* completion the variables kase and l are set as follows. */
/* kase = 1 if s(m) and e(l-1) are negligible and l.lt.m */
/* kase = 2 if s(l) is negligible and l.lt.m */
/* kase = 3 if e(l-1) is negligible, l.lt.m, and */
/* s(l), ..., s(m) are not negligible (qr step). */
/* kase = 4 if e(m-1) is negligible (convergence). */
/*< do 430 ll = 1, m >*/
i__1 = m;
for (ll = 1; ll <= i__1; ++ll) {
/*< l = m - ll >*/
l = m - ll;
/* ...exit */
/*< if (l .eq. 0) go to 440 >*/
if (l == 0) {
goto L440;
}
/*< test = cabs(s(l)) + cabs(s(l+1)) >*/
test = c_abs(&s[l]) + c_abs(&s[l + 1]);
/*< ztest = test + cabs(e(l)) >*/
ztest = test + c_abs(&e[l]);
/*< if (ztest .ne. test) go to 420 >*/
if (ztest != test) {
goto L420;
}
/*< e(l) = (0.0e0,0.0e0) >*/
i__2 = l;
e[i__2].r = (float)0., e[i__2].i = (float)0.;
/* ......exit */
/*< go to 440 >*/
goto L440;
/*< 420 continue >*/
L420:
/*< 430 continue >*/
/* L430: */
;
}
/*< 440 continue >*/
L440:
/*< if (l .ne. m - 1) go to 450 >*/
if (l != m - 1) {
goto L450;
}
/*< kase = 4 >*/
kase = 4;
/*< go to 520 >*/
goto L520;
/*< 450 continue >*/
L450:
/*< lp1 = l + 1 >*/
lp1 = l + 1;
/*< mp1 = m + 1 >*/
mp1 = m + 1;
/*< do 470 lls = lp1, mp1 >*/
i__1 = mp1;
for (lls = lp1; lls <= i__1; ++lls) {
/*< ls = m - lls + lp1 >*/
ls = m - lls + lp1;
/* ...exit */
/*< if (ls .eq. l) go to 480 >*/
if (ls == l) {
goto L480;
}
/*< test = 0.0e0 >*/
test = (float)0.;
/*< if (ls .ne. m) test = test + cabs(e(ls)) >*/
if (ls != m) {
test += c_abs(&e[ls]);
}
/*< if (ls .ne. l + 1) test = test + cabs(e(ls-1)) >*/
if (ls != l + 1) {
test += c_abs(&e[ls - 1]);
}
/*< ztest = test + cabs(s(ls)) >*/
ztest = test + c_abs(&s[ls]);
/*< if (ztest .ne. test) go to 460 >*/
if (ztest != test) {
goto L460;
}
/*< s(ls) = (0.0e0,0.0e0) >*/
i__2 = ls;
s[i__2].r = (float)0., s[i__2].i = (float)0.;
/* ......exit */
/*< go to 480 >*/
goto L480;
/*< 460 continue >*/
L460:
/*< 470 continue >*/
/* L470: */
;
}
/*< 480 continue >*/
L480:
/*< if (ls .ne. l) go to 490 >*/
if (ls != l) {
goto L490;
}
/*< kase = 3 >*/
kase = 3;
/*< go to 510 >*/
goto L510;
/*< 490 continue >*/
L490:
/*< if (ls .ne. m) go to 500 >*/
if (ls != m) {
goto L500;
}
/*< kase = 1 >*/
kase = 1;
/*< go to 510 >*/
goto L510;
/*< 500 continue >*/
L500:
/*< kase = 2 >*/
kase = 2;
/*< l = ls >*/
l = ls;
/*< 510 continue >*/
L510:
/*< 520 continue >*/
L520:
/*< l = l + 1 >*/
++l;
/* perform the task indicated by kase. */
/*< go to (530, 560, 580, 610), kase >*/
switch (kase) {
case 1: goto L530;
case 2: goto L560;
case 3: goto L580;
case 4: goto L610;
}
/* deflate negligible s(m). */
/*< 530 continue >*/
L530:
/*< mm1 = m - 1 >*/
mm1 = m - 1;
/*< f = real(e(m-1)) >*/
i__1 = m - 1;
f = e[i__1].r;
/*< e(m-1) = (0.0e0,0.0e0) >*/
i__1 = m - 1;
e[i__1].r = (float)0., e[i__1].i = (float)0.;
/*< do 550 kk = l, mm1 >*/
i__1 = mm1;
for (kk = l; kk <= i__1; ++kk) {
/*< k = mm1 - kk + l >*/
k = mm1 - kk + l;
/*< t1 = real(s(k)) >*/
i__2 = k;
t1 = s[i__2].r;
/*< call srotg(t1,f,cs,sn) >*/
srotg_(&t1, &f, &cs, &sn);
/*< s(k) = cmplx(t1,0.0e0) >*/
i__2 = k;
q__1.r = t1, q__1.i = (float)0.;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< if (k .eq. l) go to 540 >*/
if (k == l) {
goto L540;
}
/*< f = -sn*real(e(k-1)) >*/
i__2 = k - 1;
f = -sn * e[i__2].r;
/*< e(k-1) = cs*e(k-1) >*/
i__2 = k - 1;
i__3 = k - 1;
q__1.r = cs * e[i__3].r, q__1.i = cs * e[i__3].i;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< 540 continue >*/
L540:
/*< if (wantv) call csrot(p,v(1,k),1,v(1,m),1,cs,sn) >*/
if (wantv) {
csrot_(p, &v[k * v_dim1 + 1], &c__1, &v[m * v_dim1 + 1], &c__1, &
cs, &sn);
}
/*< 550 continue >*/
/* L550: */
}
/*< go to 650 >*/
goto L650;
/* split at negligible s(l). */
/*< 560 continue >*/
L560:
/*< f = real(e(l-1)) >*/
i__1 = l - 1;
f = e[i__1].r;
/*< e(l-1) = (0.0e0,0.0e0) >*/
i__1 = l - 1;
e[i__1].r = (float)0., e[i__1].i = (float)0.;
/*< do 570 k = l, m >*/
i__1 = m;
for (k = l; k <= i__1; ++k) {
/*< t1 = real(s(k)) >*/
i__2 = k;
t1 = s[i__2].r;
/*< call srotg(t1,f,cs,sn) >*/
srotg_(&t1, &f, &cs, &sn);
/*< s(k) = cmplx(t1,0.0e0) >*/
i__2 = k;
q__1.r = t1, q__1.i = (float)0.;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< f = -sn*real(e(k)) >*/
i__2 = k;
f = -sn * e[i__2].r;
/*< e(k) = cs*e(k) >*/
i__2 = k;
i__3 = k;
q__1.r = cs * e[i__3].r, q__1.i = cs * e[i__3].i;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< if (wantu) call csrot(n,u(1,k),1,u(1,l-1),1,cs,sn) >*/
if (wantu) {
csrot_(n, &u[k * u_dim1 + 1], &c__1, &u[(l - 1) * u_dim1 + 1], &
c__1, &cs, &sn);
}
/*< 570 continue >*/
/* L570: */
}
/*< go to 650 >*/
goto L650;
/* perform one qr step. */
/*< 580 continue >*/
L580:
/* calculate the shift. */
/*< >*/
/* Computing MAX */
r__1 = c_abs(&s[m]), r__2 = c_abs(&s[m - 1]), r__1 = max(r__1,r__2), r__2
= c_abs(&e[m - 1]), r__1 = max(r__1,r__2), r__2 = c_abs(&s[l]),
r__1 = max(r__1,r__2), r__2 = c_abs(&e[l]);
scale = dmax(r__1,r__2);
/*< sm = real(s(m))/scale >*/
i__1 = m;
sm = s[i__1].r / scale;
/*< smm1 = real(s(m-1))/scale >*/
i__1 = m - 1;
smm1 = s[i__1].r / scale;
/*< emm1 = real(e(m-1))/scale >*/
i__1 = m - 1;
emm1 = e[i__1].r / scale;
/*< sl = real(s(l))/scale >*/
i__1 = l;
sl = s[i__1].r / scale;
/*< el = real(e(l))/scale >*/
i__1 = l;
el = e[i__1].r / scale;
/*< b = ((smm1 + sm)*(smm1 - sm) + emm1**2)/2.0e0 >*/
/* Computing 2nd power */
r__1 = emm1;
b = ((smm1 + sm) * (smm1 - sm) + r__1 * r__1) / (float)2.;
/*< c = (sm*emm1)**2 >*/
/* Computing 2nd power */
r__1 = sm * emm1;
c__ = r__1 * r__1;
/*< shift = 0.0e0 >*/
shift = (float)0.;
/*< if (b .eq. 0.0e0 .and. c .eq. 0.0e0) go to 590 >*/
if (b == (float)0. && c__ == (float)0.) {
goto L590;
}
/*< shift = sqrt(b**2+c) >*/
/* Computing 2nd power */
r__1 = b;
shift = sqrt(r__1 * r__1 + c__);
/*< if (b .lt. 0.0e0) shift = -shift >*/
if (b < (float)0.) {
shift = -shift;
}
/*< shift = c/(b + shift) >*/
shift = c__ / (b + shift);
/*< 590 continue >*/
L590:
/*< f = (sl + sm)*(sl - sm) + shift >*/
f = (sl + sm) * (sl - sm) + shift;
/*< g = sl*el >*/
g = sl * el;
/* chase zeros. */
/*< mm1 = m - 1 >*/
mm1 = m - 1;
/*< do 600 k = l, mm1 >*/
i__1 = mm1;
for (k = l; k <= i__1; ++k) {
/*< call srotg(f,g,cs,sn) >*/
srotg_(&f, &g, &cs, &sn);
/*< if (k .ne. l) e(k-1) = cmplx(f,0.0e0) >*/
if (k != l) {
i__2 = k - 1;
q__1.r = f, q__1.i = (float)0.;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
}
/*< f = cs*real(s(k)) + sn*real(e(k)) >*/
i__2 = k;
i__3 = k;
f = cs * s[i__2].r + sn * e[i__3].r;
/*< e(k) = cs*e(k) - sn*s(k) >*/
i__2 = k;
i__3 = k;
q__2.r = cs * e[i__3].r, q__2.i = cs * e[i__3].i;
i__4 = k;
q__3.r = sn * s[i__4].r, q__3.i = sn * s[i__4].i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< g = sn*real(s(k+1)) >*/
i__2 = k + 1;
g = sn * s[i__2].r;
/*< s(k+1) = cs*s(k+1) >*/
i__2 = k + 1;
i__3 = k + 1;
q__1.r = cs * s[i__3].r, q__1.i = cs * s[i__3].i;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< if (wantv) call csrot(p,v(1,k),1,v(1,k+1),1,cs,sn) >*/
if (wantv) {
csrot_(p, &v[k * v_dim1 + 1], &c__1, &v[(k + 1) * v_dim1 + 1], &
c__1, &cs, &sn);
}
/*< call srotg(f,g,cs,sn) >*/
srotg_(&f, &g, &cs, &sn);
/*< s(k) = cmplx(f,0.0e0) >*/
i__2 = k;
q__1.r = f, q__1.i = (float)0.;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< f = cs*real(e(k)) + sn*real(s(k+1)) >*/
i__2 = k;
i__3 = k + 1;
f = cs * e[i__2].r + sn * s[i__3].r;
/*< s(k+1) = -sn*e(k) + cs*s(k+1) >*/
i__2 = k + 1;
r__1 = -sn;
i__3 = k;
q__2.r = r__1 * e[i__3].r, q__2.i = r__1 * e[i__3].i;
i__4 = k + 1;
q__3.r = cs * s[i__4].r, q__3.i = cs * s[i__4].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
s[i__2].r = q__1.r, s[i__2].i = q__1.i;
/*< g = sn*real(e(k+1)) >*/
i__2 = k + 1;
g = sn * e[i__2].r;
/*< e(k+1) = cs*e(k+1) >*/
i__2 = k + 1;
i__3 = k + 1;
q__1.r = cs * e[i__3].r, q__1.i = cs * e[i__3].i;
e[i__2].r = q__1.r, e[i__2].i = q__1.i;
/*< >*/
if (wantu && k < *n) {
csrot_(n, &u[k * u_dim1 + 1], &c__1, &u[(k + 1) * u_dim1 + 1], &
c__1, &cs, &sn);
}
/*< 600 continue >*/
/* L600: */
}
/*< e(m-1) = cmplx(f,0.0e0) >*/
i__1 = m - 1;
q__1.r = f, q__1.i = (float)0.;
e[i__1].r = q__1.r, e[i__1].i = q__1.i;
/*< iter = iter + 1 >*/
++iter;
/*< go to 650 >*/
goto L650;
/* convergence. */
/*< 610 continue >*/
L610:
/* make the singular value positive */
/*< if (real(s(l)) .ge. 0.0e0) go to 620 >*/
i__1 = l;
if (s[i__1].r >= (float)0.) {
goto L620;
}
/*< s(l) = -s(l) >*/
i__1 = l;
i__2 = l;
q__1.r = -s[i__2].r, q__1.i = -s[i__2].i;
s[i__1].r = q__1.r, s[i__1].i = q__1.i;
/*< if (wantv) call cscal(p,(-1.0e0,0.0e0),v(1,l),1) >*/
if (wantv) {
cscal_(p, &c_b53, &v[l * v_dim1 + 1], &c__1);
}
/*< 620 continue >*/
L620:
/* order the singular value. */
/*< 630 if (l .eq. mm) go to 640 >*/
L630:
if (l == mm) {
goto L640;
}
/* ...exit */
/*< if (real(s(l)) .ge. real(s(l+1))) go to 640 >*/
i__1 = l;
i__2 = l + 1;
if (s[i__1].r >= s[i__2].r) {
goto L640;
}
/*< t = s(l) >*/
i__1 = l;
t.r = s[i__1].r, t.i = s[i__1].i;
/*< s(l) = s(l+1) >*/
i__1 = l;
i__2 = l + 1;
s[i__1].r = s[i__2].r, s[i__1].i = s[i__2].i;
/*< s(l+1) = t >*/
i__1 = l + 1;
s[i__1].r = t.r, s[i__1].i = t.i;
/*< >*/
if (wantv && l < *p) {
cswap_(p, &v[l * v_dim1 + 1], &c__1, &v[(l + 1) * v_dim1 + 1], &c__1);
}
/*< >*/
if (wantu && l < *n) {
cswap_(n, &u[l * u_dim1 + 1], &c__1, &u[(l + 1) * u_dim1 + 1], &c__1);
}
/*< l = l + 1 >*/
++l;
/*< go to 630 >*/
goto L630;
/*< 640 continue >*/
L640:
/*< iter = 0 >*/
iter = 0;
/*< m = m - 1 >*/
--m;
/*< 650 continue >*/
L650:
/*< go to 400 >*/
goto L400;
/*< 660 continue >*/
L660:
/*< return >*/
return 0;
/*< end >*/
} /* csvdc_ */
doublereal scnrm2_(integer *n, complex *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
real ret_val, r__1;
/* Builtin functions */
double r_imag(complex *), sqrt(doublereal);
/* Local variables */
integer ix;
real ssq, temp, norm, scale;
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SCNRM2 returns the euclidean norm of a vector via the function */
/* name, so that */
/* SCNRM2 := sqrt( conjg( x' )*x ) */
/* -- This version written on 25-October-1982. */
/* Modified on 14-October-1993 to inline the call to CLASSQ. */
/* Sven Hammarling, Nag Ltd. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.f;
} else {
scale = 0.f;
ssq = 1.f;
/* The following loop is equivalent to this call to the LAPACK */
/* auxiliary routine: */
/* CALL CLASSQ( N, X, INCX, SCALE, SSQ ) */
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.f) {
i__3 = ix;
temp = (r__1 = x[i__3].r, dabs(r__1));
if (scale < temp) {
/* Computing 2nd power */
r__1 = scale / temp;
ssq = ssq * (r__1 * r__1) + 1.f;
scale = temp;
} else {
/* Computing 2nd power */
r__1 = temp / scale;
ssq += r__1 * r__1;
}
}
if (r_imag(&x[ix]) != 0.f) {
temp = (r__1 = r_imag(&x[ix]), dabs(r__1));
if (scale < temp) {
/* Computing 2nd power */
r__1 = scale / temp;
ssq = ssq * (r__1 * r__1) + 1.f;
scale = temp;
} else {
/* Computing 2nd power */
r__1 = temp / scale;
ssq += r__1 * r__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of SCNRM2. */
} /* scnrm2_ */
/* Subroutine */
int cla_heamv_(integer *uplo, integer *n, real *alpha, complex *a, integer *lda, complex *x, integer *incx, real *beta, real *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *), r_sign(real *, real *);
/* Local variables */
integer i__, j;
logical symb_zero__;
integer iy, jx, kx, ky, info;
real temp, safe1;
extern real slamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer ilauplo_(char *);
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (*uplo != ilauplo_("U") && *uplo != ilauplo_("L") )
{
info = 1;
}
else if (*n < 0)
{
info = 2;
}
else if (*lda < max(1,*n))
{
info = 5;
}
else if (*incx == 0)
{
info = 7;
}
else if (*incy == 0)
{
info = 10;
}
if (info != 0)
{
xerbla_("CHEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.f && *beta == 1.f)
{
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0)
{
kx = 1;
}
else
{
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0)
{
ky = 1;
}
else
{
ky = 1 - (*n - 1) * *incy;
}
/* Set SAFE1 essentially to be the underflow threshold times the */
/* number of additions in each row. */
safe1 = slamch_("Safe minimum");
safe1 = (*n + 1) * safe1;
/* Form y := alpha*abs(A)*abs(x) + beta*abs(y). */
/* The O(N^2) SYMB_ZERO tests could be replaced by O(N) queries to */
/* the inexact flag. Still doesn't help change the iteration order */
/* to per-column. */
iy = ky;
if (*incx == 1)
{
if (*uplo == ilauplo_("U"))
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (*beta == 0.f)
{
symb_zero__ = TRUE_;
y[iy] = 0.f;
}
else if (y[iy] == 0.f)
{
symb_zero__ = TRUE_;
}
else
{
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], abs(r__1));
}
if (*alpha != 0.f)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[j + i__ * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = j;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[j]), abs(r__2))) * temp;
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[i__ + j * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = j;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[j]), abs(r__2))) * temp;
}
}
if (! symb_zero__)
{
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
}
else
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (*beta == 0.f)
{
symb_zero__ = TRUE_;
y[iy] = 0.f;
}
else if (y[iy] == 0.f)
{
symb_zero__ = TRUE_;
}
else
{
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], abs(r__1));
}
if (*alpha != 0.f)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[i__ + j * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = j;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[j]), abs(r__2))) * temp;
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[j + i__ * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = j;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[j]), abs(r__2))) * temp;
}
}
if (! symb_zero__)
{
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
}
}
else
{
if (*uplo == ilauplo_("U"))
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (*beta == 0.f)
{
symb_zero__ = TRUE_;
y[iy] = 0.f;
}
else if (y[iy] == 0.f)
{
symb_zero__ = TRUE_;
}
else
{
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], abs(r__1));
}
jx = kx;
if (*alpha != 0.f)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[j + i__ * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = jx;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[jx]), abs(r__2))) * temp;
jx += *incx;
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[i__ + j * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = jx;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[jx]), abs(r__2))) * temp;
jx += *incx;
}
}
if (! symb_zero__)
{
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
}
else
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
if (*beta == 0.f)
{
symb_zero__ = TRUE_;
y[iy] = 0.f;
}
else if (y[iy] == 0.f)
{
symb_zero__ = TRUE_;
}
else
{
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], abs(r__1));
}
jx = kx;
if (*alpha != 0.f)
{
i__2 = i__;
for (j = 1;
j <= i__2;
++j)
{
i__3 = i__ + j * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[i__ + j * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = jx;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[jx]), abs(r__2))) * temp;
jx += *incx;
}
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
i__3 = j + i__ * a_dim1;
temp = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = r_imag( &a[j + i__ * a_dim1]), abs(r__2));
i__3 = j;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[ i__3].i == 0.f || temp == 0.f);
i__3 = jx;
y[iy] += *alpha * ((r__1 = x[i__3].r, abs(r__1)) + ( r__2 = r_imag(&x[jx]), abs(r__2))) * temp;
jx += *incx;
}
}
if (! symb_zero__)
{
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
}
}
return 0;
/* End of CLA_HEAMV */
}
int cggbal_(char *job, int *n, complex *a, int *lda,
complex *b, int *ldb, int *ilo, int *ihi, float *lscale,
float *rscale, float *work, int *info)
{
/* System generated locals */
int a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
float r__1, r__2, r__3;
/* Builtin functions */
double r_lg10(float *), r_imag(complex *), c_abs(complex *), r_sign(float *,
float *), pow_ri(float *, int *);
/* Local variables */
int i__, j, k, l, m;
float t;
int jc;
float ta, tb, tc;
int ir;
float ew;
int it, nr, ip1, jp1, lm1;
float cab, rab, ewc, cor, sum;
int nrp2, icab, lcab;
float beta, coef;
int irab, lrab;
float basl, cmax;
extern double sdot_(int *, float *, int *, float *, int *);
float coef2, coef5, gamma, alpha;
extern int lsame_(char *, char *);
extern int sscal_(int *, float *, float *, int *);
float sfmin;
extern int cswap_(int *, complex *, int *,
complex *, int *);
float sfmax;
int iflow, kount;
extern int saxpy_(int *, float *, float *, int *,
float *, int *);
float pgamma;
extern int icamax_(int *, complex *, int *);
extern double slamch_(char *);
extern int csscal_(int *, float *, complex *, int
*), xerbla_(char *, int *);
int lsfmin, lsfmax;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGGBAL balances a pair of general complex matrices (A,B). This */
/* involves, first, permuting A and B by similarity transformations to */
/* isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N */
/* elements on the diagonal; and second, applying a diagonal similarity */
/* transformation to rows and columns ILO to IHI to make the rows */
/* and columns as close in norm as possible. Both steps are optional. */
/* Balancing may reduce the 1-norm of the matrices, and improve the */
/* accuracy of the computed eigenvalues and/or eigenvectors in the */
/* generalized eigenvalue problem A*x = lambda*B*x. */
/* Arguments */
/* ========= */
/* JOB (input) CHARACTER*1 */
/* Specifies the operations to be performed on A and B: */
/* = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 */
/* and RSCALE(I) = 1.0 for i=1,...,N; */
/* = 'P': permute only; */
/* = 'S': scale only; */
/* = 'B': both permute and scale. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the input matrix A. */
/* On exit, A is overwritten by the balanced matrix. */
/* If JOB = 'N', A is not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* B (input/output) COMPLEX array, dimension (LDB,N) */
/* On entry, the input matrix B. */
/* On exit, B is overwritten by the balanced matrix. */
/* If JOB = 'N', B is not referenced. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,N). */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are set to ints such that on exit */
/* A(i,j) = 0 and B(i,j) = 0 if i > j and */
/* j = 1,...,ILO-1 or i = IHI+1,...,N. */
/* If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
/* LSCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* to the left side of A and B. If P(j) is the index of the */
/* row interchanged with row j, and D(j) is the scaling factor */
/* applied to row j, then */
/* LSCALE(j) = P(j) for J = 1,...,ILO-1 */
/* = D(j) for J = ILO,...,IHI */
/* = P(j) for J = IHI+1,...,N. */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* RSCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* to the right side of A and B. If P(j) is the index of the */
/* column interchanged with column j, and D(j) is the scaling */
/* factor applied to column j, then */
/* RSCALE(j) = P(j) for J = 1,...,ILO-1 */
/* = D(j) for J = ILO,...,IHI */
/* = P(j) for J = IHI+1,...,N. */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* WORK (workspace) REAL array, dimension (lwork) */
/* lwork must be at least MAX(1,6*N) when JOB = 'S' or 'B', and */
/* at least 1 when JOB = 'N' or 'P'. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* See R.C. WARD, Balancing the generalized eigenvalue problem, */
/* SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--lscale;
--rscale;
--work;
/* Function Body */
*info = 0;
if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
&& ! lsame_(job, "B")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < MAX(1,*n)) {
*info = -4;
} else if (*ldb < MAX(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGGBAL", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*ilo = 1;
*ihi = *n;
return 0;
}
if (*n == 1) {
*ilo = 1;
*ihi = *n;
lscale[1] = 1.f;
rscale[1] = 1.f;
return 0;
}
if (lsame_(job, "N")) {
*ilo = 1;
*ihi = *n;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
lscale[i__] = 1.f;
rscale[i__] = 1.f;
/* L10: */
}
return 0;
}
k = 1;
l = *n;
if (lsame_(job, "S")) {
goto L190;
}
goto L30;
/* Permute the matrices A and B to isolate the eigenvalues. */
/* Find row with one nonzero in columns 1 through L */
L20:
l = lm1;
if (l != 1) {
goto L30;
}
rscale[1] = 1.f;
lscale[1] = 1.f;
goto L190;
L30:
lm1 = l - 1;
for (i__ = l; i__ >= 1; --i__) {
i__1 = lm1;
for (j = 1; j <= i__1; ++j) {
jp1 = j + 1;
i__2 = i__ + j * a_dim1;
i__3 = i__ + j * b_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f || (b[i__3].r != 0.f ||
b[i__3].i != 0.f)) {
goto L50;
}
/* L40: */
}
j = l;
goto L70;
L50:
i__1 = l;
for (j = jp1; j <= i__1; ++j) {
i__2 = i__ + j * a_dim1;
i__3 = i__ + j * b_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f || (b[i__3].r != 0.f ||
b[i__3].i != 0.f)) {
goto L80;
}
/* L60: */
}
j = jp1 - 1;
L70:
m = l;
iflow = 1;
goto L160;
L80:
;
}
goto L100;
/* Find column with one nonzero in rows K through N */
L90:
++k;
L100:
i__1 = l;
for (j = k; j <= i__1; ++j) {
i__2 = lm1;
for (i__ = k; i__ <= i__2; ++i__) {
ip1 = i__ + 1;
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * b_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r != 0.f ||
b[i__4].i != 0.f)) {
goto L120;
}
/* L110: */
}
i__ = l;
goto L140;
L120:
i__2 = l;
for (i__ = ip1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * b_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r != 0.f ||
b[i__4].i != 0.f)) {
goto L150;
}
/* L130: */
}
i__ = ip1 - 1;
L140:
m = k;
iflow = 2;
goto L160;
L150:
;
}
goto L190;
/* Permute rows M and I */
L160:
lscale[m] = (float) i__;
if (i__ == m) {
goto L170;
}
i__1 = *n - k + 1;
cswap_(&i__1, &a[i__ + k * a_dim1], lda, &a[m + k * a_dim1], lda);
i__1 = *n - k + 1;
cswap_(&i__1, &b[i__ + k * b_dim1], ldb, &b[m + k * b_dim1], ldb);
/* Permute columns M and J */
L170:
rscale[m] = (float) j;
if (j == m) {
goto L180;
}
cswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
cswap_(&l, &b[j * b_dim1 + 1], &c__1, &b[m * b_dim1 + 1], &c__1);
L180:
switch (iflow) {
case 1: goto L20;
case 2: goto L90;
}
L190:
*ilo = k;
*ihi = l;
if (lsame_(job, "P")) {
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
lscale[i__] = 1.f;
rscale[i__] = 1.f;
/* L195: */
}
return 0;
}
if (*ilo == *ihi) {
return 0;
}
/* Balance the submatrix in rows ILO to IHI. */
nr = *ihi - *ilo + 1;
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
rscale[i__] = 0.f;
lscale[i__] = 0.f;
work[i__] = 0.f;
work[i__ + *n] = 0.f;
work[i__ + (*n << 1)] = 0.f;
work[i__ + *n * 3] = 0.f;
work[i__ + (*n << 2)] = 0.f;
work[i__ + *n * 5] = 0.f;
/* L200: */
}
/* Compute right side vector in resulting linear equations */
basl = r_lg10(&c_b36);
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
i__2 = *ihi;
for (j = *ilo; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
if (a[i__3].r == 0.f && a[i__3].i == 0.f) {
ta = 0.f;
goto L210;
}
i__3 = i__ + j * a_dim1;
r__3 = (r__1 = a[i__3].r, ABS(r__1)) + (r__2 = r_imag(&a[i__ + j
* a_dim1]), ABS(r__2));
ta = r_lg10(&r__3) / basl;
L210:
i__3 = i__ + j * b_dim1;
if (b[i__3].r == 0.f && b[i__3].i == 0.f) {
tb = 0.f;
goto L220;
}
i__3 = i__ + j * b_dim1;
r__3 = (r__1 = b[i__3].r, ABS(r__1)) + (r__2 = r_imag(&b[i__ + j
* b_dim1]), ABS(r__2));
tb = r_lg10(&r__3) / basl;
L220:
work[i__ + (*n << 2)] = work[i__ + (*n << 2)] - ta - tb;
work[j + *n * 5] = work[j + *n * 5] - ta - tb;
/* L230: */
}
/* L240: */
}
coef = 1.f / (float) (nr << 1);
coef2 = coef * coef;
coef5 = coef2 * .5f;
nrp2 = nr + 2;
beta = 0.f;
it = 1;
/* Start generalized conjugate gradient iteration */
L250:
gamma = sdot_(&nr, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + (*n << 2)]
, &c__1) + sdot_(&nr, &work[*ilo + *n * 5], &c__1, &work[*ilo + *
n * 5], &c__1);
ew = 0.f;
ewc = 0.f;
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
ew += work[i__ + (*n << 2)];
ewc += work[i__ + *n * 5];
/* L260: */
}
/* Computing 2nd power */
r__1 = ew;
/* Computing 2nd power */
r__2 = ewc;
/* Computing 2nd power */
r__3 = ew - ewc;
gamma = coef * gamma - coef2 * (r__1 * r__1 + r__2 * r__2) - coef5 * (
r__3 * r__3);
if (gamma == 0.f) {
goto L350;
}
if (it != 1) {
beta = gamma / pgamma;
}
t = coef5 * (ewc - ew * 3.f);
tc = coef5 * (ew - ewc * 3.f);
sscal_(&nr, &beta, &work[*ilo], &c__1);
sscal_(&nr, &beta, &work[*ilo + *n], &c__1);
saxpy_(&nr, &coef, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + *n], &
c__1);
saxpy_(&nr, &coef, &work[*ilo + *n * 5], &c__1, &work[*ilo], &c__1);
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
work[i__] += tc;
work[i__ + *n] += t;
/* L270: */
}
/* Apply matrix to vector */
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
kount = 0;
sum = 0.f;
i__2 = *ihi;
for (j = *ilo; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
if (a[i__3].r == 0.f && a[i__3].i == 0.f) {
goto L280;
}
++kount;
sum += work[j];
L280:
i__3 = i__ + j * b_dim1;
if (b[i__3].r == 0.f && b[i__3].i == 0.f) {
goto L290;
}
++kount;
sum += work[j];
L290:
;
}
work[i__ + (*n << 1)] = (float) kount * work[i__ + *n] + sum;
/* L300: */
}
i__1 = *ihi;
for (j = *ilo; j <= i__1; ++j) {
kount = 0;
sum = 0.f;
i__2 = *ihi;
for (i__ = *ilo; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
if (a[i__3].r == 0.f && a[i__3].i == 0.f) {
goto L310;
}
++kount;
sum += work[i__ + *n];
L310:
i__3 = i__ + j * b_dim1;
if (b[i__3].r == 0.f && b[i__3].i == 0.f) {
goto L320;
}
++kount;
sum += work[i__ + *n];
L320:
;
}
work[j + *n * 3] = (float) kount * work[j] + sum;
/* L330: */
}
sum = sdot_(&nr, &work[*ilo + *n], &c__1, &work[*ilo + (*n << 1)], &c__1)
+ sdot_(&nr, &work[*ilo], &c__1, &work[*ilo + *n * 3], &c__1);
alpha = gamma / sum;
/* Determine correction to current iteration */
cmax = 0.f;
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
cor = alpha * work[i__ + *n];
if (ABS(cor) > cmax) {
cmax = ABS(cor);
}
lscale[i__] += cor;
cor = alpha * work[i__];
if (ABS(cor) > cmax) {
cmax = ABS(cor);
}
rscale[i__] += cor;
/* L340: */
}
if (cmax < .5f) {
goto L350;
}
r__1 = -alpha;
saxpy_(&nr, &r__1, &work[*ilo + (*n << 1)], &c__1, &work[*ilo + (*n << 2)]
, &c__1);
r__1 = -alpha;
saxpy_(&nr, &r__1, &work[*ilo + *n * 3], &c__1, &work[*ilo + *n * 5], &
c__1);
pgamma = gamma;
++it;
if (it <= nrp2) {
goto L250;
}
/* End generalized conjugate gradient iteration */
L350:
sfmin = slamch_("S");
sfmax = 1.f / sfmin;
lsfmin = (int) (r_lg10(&sfmin) / basl + 1.f);
lsfmax = (int) (r_lg10(&sfmax) / basl);
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
i__2 = *n - *ilo + 1;
irab = icamax_(&i__2, &a[i__ + *ilo * a_dim1], lda);
rab = c_abs(&a[i__ + (irab + *ilo - 1) * a_dim1]);
i__2 = *n - *ilo + 1;
irab = icamax_(&i__2, &b[i__ + *ilo * b_dim1], ldb);
/* Computing MAX */
r__1 = rab, r__2 = c_abs(&b[i__ + (irab + *ilo - 1) * b_dim1]);
rab = MAX(r__1,r__2);
r__1 = rab + sfmin;
lrab = (int) (r_lg10(&r__1) / basl + 1.f);
ir = lscale[i__] + r_sign(&c_b72, &lscale[i__]);
/* Computing MIN */
i__2 = MAX(ir,lsfmin), i__2 = MIN(i__2,lsfmax), i__3 = lsfmax - lrab;
ir = MIN(i__2,i__3);
lscale[i__] = pow_ri(&c_b36, &ir);
icab = icamax_(ihi, &a[i__ * a_dim1 + 1], &c__1);
cab = c_abs(&a[icab + i__ * a_dim1]);
icab = icamax_(ihi, &b[i__ * b_dim1 + 1], &c__1);
/* Computing MAX */
r__1 = cab, r__2 = c_abs(&b[icab + i__ * b_dim1]);
cab = MAX(r__1,r__2);
r__1 = cab + sfmin;
lcab = (int) (r_lg10(&r__1) / basl + 1.f);
jc = rscale[i__] + r_sign(&c_b72, &rscale[i__]);
/* Computing MIN */
i__2 = MAX(jc,lsfmin), i__2 = MIN(i__2,lsfmax), i__3 = lsfmax - lcab;
jc = MIN(i__2,i__3);
rscale[i__] = pow_ri(&c_b36, &jc);
/* L360: */
}
/* Row scaling of matrices A and B */
i__1 = *ihi;
for (i__ = *ilo; i__ <= i__1; ++i__) {
i__2 = *n - *ilo + 1;
csscal_(&i__2, &lscale[i__], &a[i__ + *ilo * a_dim1], lda);
i__2 = *n - *ilo + 1;
csscal_(&i__2, &lscale[i__], &b[i__ + *ilo * b_dim1], ldb);
/* L370: */
}
/* Column scaling of matrices A and B */
i__1 = *ihi;
for (j = *ilo; j <= i__1; ++j) {
csscal_(ihi, &rscale[j], &a[j * a_dim1 + 1], &c__1);
csscal_(ihi, &rscale[j], &b[j * b_dim1 + 1], &c__1);
/* L380: */
}
return 0;
/* End of CGGBAL */
} /* cggbal_ */
/* Subroutine */ int ctpt05_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *b, integer *ldb, complex *x,
integer *ldx, complex *xact, integer *ldxact, real *ferr, real *berr,
real *reslts)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, xact_dim1, xact_offset, i__1,
i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1, q__2;
/* Local variables */
integer i__, j, k, jc, ifu;
real eps, tmp, diff, axbi;
integer imax;
real unfl, ovfl;
logical unit;
logical upper;
real xnorm;
real errbnd;
logical notran;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPT05 tests the error bounds from iterative refinement for the */
/* computed solution to a system of equations A*X = B, where A is a */
/* triangular matrix in packed storage format. */
/* RESLTS(1) = test of the error bound */
/* = norm(X - XACT) / ( norm(X) * FERR ) */
/* A large value is returned if this ratio is not less than one. */
/* RESLTS(2) = residual from the iterative refinement routine */
/* = the maximum of BERR / ( (n+1)*EPS + (*) ), where */
/* (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations. */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A'* X = B (Transpose) */
/* = 'C': A'* X = B (Conjugate transpose = Transpose) */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The number of rows of the matrices X, B, and XACT, and the */
/* order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of columns of the matrices X, B, and XACT. */
/* NRHS >= 0. */
/* AP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The upper or lower triangular matrix A, packed columnwise in */
/* a linear array. The j-th column of A is stored in the array */
/* AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 1. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side vectors for the system of linear */
/* equations. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input) COMPLEX array, dimension (LDX,NRHS) */
/* The computed solution vectors. Each vector is stored as a */
/* column of the matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* XACT (input) COMPLEX array, dimension (LDX,NRHS) */
/* The exact solution vectors. Each vector is stored as a */
/* column of the matrix XACT. */
/* LDXACT (input) INTEGER */
/* The leading dimension of the array XACT. LDXACT >= max(1,N). */
/* FERR (input) REAL array, dimension (NRHS) */
/* The estimated forward error bounds for each solution vector */
/* X. If XTRUE is the true solution, FERR bounds the magnitude */
/* of the largest entry in (X - XTRUE) divided by the magnitude */
/* of the largest entry in X. */
/* BERR (input) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector (i.e., the smallest relative change in any entry of A */
/* or B that makes X an exact solution). */
/* RESLTS (output) REAL array, dimension (2) */
/* The maximum over the NRHS solution vectors of the ratios: */
/* RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) */
/* RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 or NRHS = 0. */
/* Parameter adjustments */
--ap;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
xact_dim1 = *ldxact;
xact_offset = 1 + xact_dim1;
xact -= xact_offset;
--ferr;
--berr;
--reslts;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
reslts[1] = 0.f;
reslts[2] = 0.f;
return 0;
}
eps = slamch_("Epsilon");
unfl = slamch_("Safe minimum");
ovfl = 1.f / unfl;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
unit = lsame_(diag, "U");
/* Test 1: Compute the maximum of */
/* norm(X - XACT) / ( norm(X) * FERR ) */
/* over all the vectors X and XACT using the infinity-norm. */
errbnd = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
imax = icamax_(n, &x[j * x_dim1 + 1], &c__1);
/* Computing MAX */
i__2 = imax + j * x_dim1;
r__3 = (r__1 = x[i__2].r, dabs(r__1)) + (r__2 = r_imag(&x[imax + j *
x_dim1]), dabs(r__2));
xnorm = dmax(r__3,unfl);
diff = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = i__ + j * xact_dim1;
q__2.r = x[i__3].r - xact[i__4].r, q__2.i = x[i__3].i - xact[i__4]
.i;
q__1.r = q__2.r, q__1.i = q__2.i;
/* Computing MAX */
r__3 = diff, r__4 = (r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&
q__1), dabs(r__2));
diff = dmax(r__3,r__4);
/* L10: */
}
if (xnorm > 1.f) {
goto L20;
} else if (diff <= ovfl * xnorm) {
goto L20;
} else {
errbnd = 1.f / eps;
goto L30;
}
L20:
if (diff / xnorm <= ferr[j]) {
/* Computing MAX */
r__1 = errbnd, r__2 = diff / xnorm / ferr[j];
errbnd = dmax(r__1,r__2);
} else {
errbnd = 1.f / eps;
}
L30:
;
}
reslts[1] = errbnd;
/* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where */
/* (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
ifu = 0;
if (unit) {
ifu = 1;
}
i__1 = *nrhs;
for (k = 1; k <= i__1; ++k) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
tmp = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ + k *
b_dim1]), dabs(r__2));
if (upper) {
jc = (i__ - 1) * i__ / 2;
if (! notran) {
i__3 = i__ - ifu;
for (j = 1; j <= i__3; ++j) {
i__4 = jc + j;
i__5 = j + k * x_dim1;
tmp += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[jc + j]), dabs(r__2))) * ((r__3 =
x[i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[j
+ k * x_dim1]), dabs(r__4)));
/* L40: */
}
if (unit) {
i__3 = i__ + k * x_dim1;
tmp += (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + k * x_dim1]), dabs(r__2));
}
} else {
jc += i__;
if (unit) {
i__3 = i__ + k * x_dim1;
tmp += (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + k * x_dim1]), dabs(r__2));
jc += i__;
}
i__3 = *n;
for (j = i__ + ifu; j <= i__3; ++j) {
i__4 = jc;
i__5 = j + k * x_dim1;
tmp += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[jc]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[j +
k * x_dim1]), dabs(r__4)));
jc += j;
/* L50: */
}
}
} else {
if (notran) {
jc = i__;
i__3 = i__ - ifu;
for (j = 1; j <= i__3; ++j) {
i__4 = jc;
i__5 = j + k * x_dim1;
tmp += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[jc]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[j +
k * x_dim1]), dabs(r__4)));
jc = jc + *n - j;
/* L60: */
}
if (unit) {
i__3 = i__ + k * x_dim1;
tmp += (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + k * x_dim1]), dabs(r__2));
}
} else {
jc = (i__ - 1) * (*n - i__) + i__ * (i__ + 1) / 2;
if (unit) {
i__3 = i__ + k * x_dim1;
tmp += (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + k * x_dim1]), dabs(r__2));
}
i__3 = *n;
for (j = i__ + ifu; j <= i__3; ++j) {
i__4 = jc + j - i__;
i__5 = j + k * x_dim1;
tmp += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[jc + j - i__]), dabs(r__2))) * ((
r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[j + k * x_dim1]), dabs(r__4)));
/* L70: */
}
}
}
if (i__ == 1) {
axbi = tmp;
} else {
axbi = dmin(axbi,tmp);
}
/* L80: */
}
/* Computing MAX */
r__1 = axbi, r__2 = (*n + 1) * unfl;
tmp = berr[k] / ((*n + 1) * eps + (*n + 1) * unfl / dmax(r__1,r__2));
if (k == 1) {
reslts[2] = tmp;
} else {
reslts[2] = dmax(reslts[2],tmp);
}
/* L90: */
}
return 0;
/* End of CTPT05 */
} /* ctpt05_ */
/* Subroutine */ int cggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, complex *a, integer *lda, complex *b, integer
*ldb, real *tola, real *tolb, integer *k, integer *l, complex *u,
integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq,
integer *iwork, real *rwork, complex *tau, complex *work, integer *
info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CGGSVP computes unitary matrices U, V and Q such that
N-K-L K L
U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V'*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the
conjugate transpose of Z.
This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
CGGSVD.
Arguments
=========
JOBU (input) CHARACTER*1
= 'U': Unitary matrix U is computed;
= 'N': U is not computed.
JOBV (input) CHARACTER*1
= 'V': Unitary matrix V is computed;
= 'N': V is not computed.
JOBQ (input) CHARACTER*1
= 'Q': Unitary matrix Q is computed;
= 'N': Q is not computed.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
P (input) INTEGER
The number of rows of the matrix B. P >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TOLA (input) REAL
TOLB (input) REAL
TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.
K (output) INTEGER
L (output) INTEGER
On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A',B')'.
U (output) COMPLEX array, dimension (LDU,M)
If JOBU = 'U', U contains the unitary matrix U.
If JOBU = 'N', U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = 'U'; LDU >= 1 otherwise.
V (output) COMPLEX array, dimension (LDV,M)
If JOBV = 'V', V contains the unitary matrix V.
If JOBV = 'N', V is not referenced.
LDV (input) INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = 'V'; LDV >= 1 otherwise.
Q (output) COMPLEX array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the unitary matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK (workspace) INTEGER array, dimension (N)
RWORK (workspace) REAL array, dimension (2*N)
TAU (workspace) COMPLEX array, dimension (N)
WORK (workspace) COMPLEX array, dimension (max(3*N,M,P))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The subroutine uses LAPACK subroutine CGEQPF for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.
=====================================================================
Test the input parameters
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
static logical wantq, wantu, wantv;
extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cgerq2_(integer *,
integer *, complex *, integer *, complex *, complex *, integer *),
cung2r_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *), cunm2r_(char *, char *, integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, complex *, integer *), cunmr2_(char
*, char *, integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, complex *, integer *), cgeqpf_(integer *, integer *, complex *, integer *,
integer *, complex *, complex *, real *, integer *), clacpy_(char
*, integer *, integer *, complex *, integer *, complex *, integer
*), claset_(char *, integer *, integer *, complex *,
complex *, complex *, integer *), xerbla_(char *, integer
*), clapmt_(logical *, integer *, integer *, complex *,
integer *, integer *);
static logical forwrd;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1
#define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)]
#define v_subscr(a_1,a_2) (a_2)*v_dim1 + a_1
#define v_ref(a_1,a_2) v[v_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--iwork;
--rwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
forwrd = TRUE_;
*info = 0;
if (! (wantu || lsame_(jobu, "N"))) {
*info = -1;
} else if (! (wantv || lsame_(jobv, "N"))) {
*info = -2;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*p < 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*m)) {
*info = -8;
} else if (*ldb < max(1,*p)) {
*info = -10;
} else if (*ldu < 1 || wantu && *ldu < *m) {
*info = -16;
} else if (*ldv < 1 || wantv && *ldv < *p) {
*info = -18;
} else if (*ldq < 1 || wantq && *ldq < *n) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGGSVP", &i__1);
return 0;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 )
( 0 0 ) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L10: */
}
cgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], &rwork[1],
info);
/* Update A := A*P */
clapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
*l = 0;
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = b_subscr(i__, i__);
if ((r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(i__, i__)),
dabs(r__2)) > *tolb) {
++(*l);
}
/* L20: */
}
if (wantv) {
/* Copy the details of V, and form V. */
claset_("Full", p, p, &c_b1, &c_b1, &v[v_offset], ldv);
if (*p > 1) {
i__1 = *p - 1;
clacpy_("Lower", &i__1, n, &b_ref(2, 1), ldb, &v_ref(2, 1), ldv);
}
i__1 = min(*p,*n);
cung2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
}
/* Clean up B */
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
if (*p > *l) {
i__1 = *p - *l;
claset_("Full", &i__1, n, &c_b1, &c_b1, &b_ref(*l + 1, 1), ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
claset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
clapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z */
cgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
cunmr2_("Right", "Conjugate transpose", m, n, l, &b[b_offset], ldb, &
tau[1], &a[a_offset], lda, &work[1], info);
if (wantq) {
/* Update Q := Q*Z' */
cunmr2_("Right", "Conjugate transpose", n, n, l, &b[b_offset],
ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up B */
i__1 = *n - *l;
claset_("Full", l, &i__1, &c_b1, &c_b1, &b[b_offset], ldb);
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
}
/* Let N-L L
A = ( A11 A12 ) M,
then the following does the complete QR decomposition of A11:
A11 = U*( 0 T12 )*P1'
( 0 0 ) */
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L70: */
}
i__1 = *n - *l;
cgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], &rwork[
1], info);
/* Determine the effective rank of A11 */
*k = 0;
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = a_subscr(i__, i__);
if ((r__1 = a[i__2].r, dabs(r__1)) + (r__2 = r_imag(&a_ref(i__, i__)),
dabs(r__2)) > *tola) {
++(*k);
}
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
cunm2r_("Left", "Conjugate transpose", m, l, &i__1, &a[a_offset], lda, &
tau[1], &a_ref(1, *n - *l + 1), lda, &work[1], info);
if (wantu) {
/* Copy the details of U, and form U */
claset_("Full", m, m, &c_b1, &c_b1, &u[u_offset], ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
clacpy_("Lower", &i__1, &i__2, &a_ref(2, 1), lda, &u_ref(2, 1),
ldu);
}
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
cung2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
}
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
clapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
}
/* Clean up A: set the strictly lower triangular part of
A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
claset_("Full", &i__1, &i__2, &c_b1, &c_b1, &a_ref(*k + 1, 1), lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
cgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
i__1 = *n - *l;
cunmr2_("Right", "Conjugate transpose", n, &i__1, k, &a[a_offset],
lda, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up A */
i__1 = *n - *l - *k;
claset_("Full", k, &i__1, &c_b1, &c_b1, &a[a_offset], lda);
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L110: */
}
/* L120: */
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
cgeqr2_(&i__1, l, &a_ref(*k + 1, *n - *l + 1), lda, &tau[1], &work[1],
info);
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
cunm2r_("Right", "No transpose", m, &i__1, &i__2, &a_ref(*k + 1, *
n - *l + 1), lda, &tau[1], &u_ref(1, *k + 1), ldu, &work[
1], info);
}
/* Clean up */
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of CGGSVP */
} /* cggsvp_ */
/* Subroutine */ int ctprfs_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *b, integer *ldb, complex *x,
integer *ldx, real *ferr, real *berr, complex *work, real *rwork,
integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s;
integer kc;
real xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *);
logical upper;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *), clacn2_(
integer *, complex *, complex *, real *, integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical notran;
char transn[1], transt[1];
logical nounit;
real lstres;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPRFS provides error bounds and backward error estimates for the */
/* solution to a system of linear equations with a triangular packed */
/* coefficient matrix. */
/* The solution matrix X must be computed by CTPTRS or some other */
/* means before entering this routine. CTPRFS does not do iterative */
/* refinement because doing so cannot improve the backward error. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose) */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The upper or lower triangular matrix A, packed columnwise in */
/* a linear array. The j-th column of A is stored in the array */
/* AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 1. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input) COMPLEX array, dimension (LDX,NRHS) */
/* The solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldx < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ctpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
caxpy_(n, &q__1, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L20: */
}
if (notran) {
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - 1]), dabs(
r__2))) * xk;
/* L30: */
}
kc += k;
/* L40: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - 1]), dabs(
r__2))) * xk;
/* L50: */
}
rwork[k] += xk;
kc += k;
/* L60: */
}
}
} else {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - k]), dabs(
r__2))) * xk;
/* L70: */
}
kc = kc + *n - k + 1;
/* L80: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - k]), dabs(
r__2))) * xk;
/* L90: */
}
rwork[k] += xk;
kc = kc + *n - k + 1;
/* L100: */
}
}
}
} else {
/* Compute abs(A**H)*abs(X) + abs(B). */
if (upper) {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - 1]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L110: */
}
rwork[k] += s;
kc += k;
/* L120: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
s = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - 1]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L130: */
}
rwork[k] += s;
kc += k;
/* L140: */
}
}
} else {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - k]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L150: */
}
rwork[k] += s;
kc = kc + *n - k + 1;
/* L160: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
s = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - k]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L170: */
}
rwork[k] += s;
kc = kc + *n - k + 1;
/* L180: */
}
}
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L190: */
}
berr[j] = s;
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(op(A)))* */
/* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(op(A)) is the inverse of op(A) */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(op(A)) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L200: */
}
kase = 0;
L210:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
ctpsv_(uplo, transt, diag, n, &ap[1], &work[1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L220: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L230: */
}
ctpsv_(uplo, transn, diag, n, &ap[1], &work[1], &c__1);
}
goto L210;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L240: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L250: */
}
return 0;
/* End of CTPRFS */
} /* ctprfs_ */
int classq_(int *n, complex *x, int *incx, float *
scale, float *sumsq)
{
/* System generated locals */
int i__1, i__2, i__3;
float r__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
int ix;
float temp1;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLASSQ returns the values scl and ssq such that */
/* ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, */
/* where x( i ) = ABS( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is */
/* assumed to be at least unity and the value of ssq will then satisfy */
/* 1.0 .le. ssq .le. ( sumsq + 2*n ). */
/* scale is assumed to be non-negative and scl returns the value */
/* scl = MAX( scale, ABS( float( x( i ) ) ), ABS( aimag( x( i ) ) ) ), */
/* i */
/* scale and sumsq must be supplied in SCALE and SUMSQ respectively. */
/* SCALE and SUMSQ are overwritten by scl and ssq respectively. */
/* The routine makes only one pass through the vector X. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of elements to be used from the vector X. */
/* X (input) COMPLEX array, dimension (N) */
/* The vector x as described above. */
/* x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. */
/* INCX (input) INTEGER */
/* The increment between successive values of the vector X. */
/* INCX > 0. */
/* SCALE (input/output) REAL */
/* On entry, the value scale in the equation above. */
/* On exit, SCALE is overwritten with the value scl . */
/* SUMSQ (input/output) REAL */
/* On entry, the value sumsq in the equation above. */
/* On exit, SUMSQ is overwritten with the value ssq . */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--x;
/* Function Body */
if (*n > 0) {
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.f) {
i__3 = ix;
temp1 = (r__1 = x[i__3].r, ABS(r__1));
if (*scale < temp1) {
/* Computing 2nd power */
r__1 = *scale / temp1;
*sumsq = *sumsq * (r__1 * r__1) + 1;
*scale = temp1;
} else {
/* Computing 2nd power */
r__1 = temp1 / *scale;
*sumsq += r__1 * r__1;
}
}
if (r_imag(&x[ix]) != 0.f) {
temp1 = (r__1 = r_imag(&x[ix]), ABS(r__1));
if (*scale < temp1) {
/* Computing 2nd power */
r__1 = *scale / temp1;
*sumsq = *sumsq * (r__1 * r__1) + 1;
*scale = temp1;
} else {
/* Computing 2nd power */
r__1 = temp1 / *scale;
*sumsq += r__1 * r__1;
}
}
/* L10: */
}
}
return 0;
/* End of CLASSQ */
} /* classq_ */
/* Subroutine */ int cgttrf_(integer *n, complex *dl, complex *d__, complex *
du, complex *du2, integer *ipiv, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
complex q__1, q__2;
/* Builtin functions */
double r_imag(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
integer i__;
complex fact, temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGTTRF computes an LU factorization of a complex tridiagonal matrix A */
/* using elimination with partial pivoting and row interchanges. */
/* The factorization has the form */
/* A = L * U */
/* where L is a product of permutation and unit lower bidiagonal */
/* matrices and U is upper triangular with nonzeros in only the main */
/* diagonal and first two superdiagonals. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* DL (input/output) COMPLEX array, dimension (N-1) */
/* On entry, DL must contain the (n-1) sub-diagonal elements of */
/* A. */
/* On exit, DL is overwritten by the (n-1) multipliers that */
/* define the matrix L from the LU factorization of A. */
/* D (input/output) COMPLEX array, dimension (N) */
/* On entry, D must contain the diagonal elements of A. */
/* On exit, D is overwritten by the n diagonal elements of the */
/* upper triangular matrix U from the LU factorization of A. */
/* DU (input/output) COMPLEX array, dimension (N-1) */
/* On entry, DU must contain the (n-1) super-diagonal elements */
/* of A. */
/* On exit, DU is overwritten by the (n-1) elements of the first */
/* super-diagonal of U. */
/* DU2 (output) COMPLEX array, dimension (N-2) */
/* On exit, DU2 is overwritten by the (n-2) elements of the */
/* second super-diagonal of U. */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices; for 1 <= i <= n, row i of the matrix was */
/* interchanged with row IPIV(i). IPIV(i) will always be either */
/* i or i+1; IPIV(i) = i indicates a row interchange was not */
/* required. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -k, the k-th argument had an illegal value */
/* > 0: if INFO = k, U(k,k) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, and division by zero will occur if it is used */
/* to solve a system of equations. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ipiv;
--du2;
--du;
--d__;
--dl;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
i__1 = -(*info);
xerbla_("CGTTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Initialize IPIV(i) = i and DU2(i) = 0 */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
ipiv[i__] = i__;
/* L10: */
}
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
du2[i__2].r = 0.f, du2[i__2].i = 0.f;
/* L20: */
}
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) >= (r__3 = dl[i__3].r, dabs(r__3)) + (r__4 =
r_imag(&dl[i__]), dabs(r__4))) {
/* No row interchange required, eliminate DL(I) */
i__2 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) != 0.f) {
c_div(&q__1, &dl[i__], &d__[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__2 = i__;
dl[i__2].r = fact.r, dl[i__2].i = fact.i;
i__2 = i__ + 1;
i__3 = i__ + 1;
i__4 = i__;
q__2.r = fact.r * du[i__4].r - fact.i * du[i__4].i, q__2.i =
fact.r * du[i__4].i + fact.i * du[i__4].r;
q__1.r = d__[i__3].r - q__2.r, q__1.i = d__[i__3].i - q__2.i;
d__[i__2].r = q__1.r, d__[i__2].i = q__1.i;
}
} else {
/* Interchange rows I and I+1, eliminate DL(I) */
c_div(&q__1, &d__[i__], &dl[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__2 = i__;
i__3 = i__;
d__[i__2].r = dl[i__3].r, d__[i__2].i = dl[i__3].i;
i__2 = i__;
dl[i__2].r = fact.r, dl[i__2].i = fact.i;
i__2 = i__;
temp.r = du[i__2].r, temp.i = du[i__2].i;
i__2 = i__;
i__3 = i__ + 1;
du[i__2].r = d__[i__3].r, du[i__2].i = d__[i__3].i;
i__2 = i__ + 1;
i__3 = i__ + 1;
q__2.r = fact.r * d__[i__3].r - fact.i * d__[i__3].i, q__2.i =
fact.r * d__[i__3].i + fact.i * d__[i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
d__[i__2].r = q__1.r, d__[i__2].i = q__1.i;
i__2 = i__;
i__3 = i__ + 1;
du2[i__2].r = du[i__3].r, du2[i__2].i = du[i__3].i;
i__2 = i__ + 1;
q__2.r = -fact.r, q__2.i = -fact.i;
i__3 = i__ + 1;
q__1.r = q__2.r * du[i__3].r - q__2.i * du[i__3].i, q__1.i =
q__2.r * du[i__3].i + q__2.i * du[i__3].r;
du[i__2].r = q__1.r, du[i__2].i = q__1.i;
ipiv[i__] = i__ + 1;
}
/* L30: */
}
if (*n > 1) {
i__ = *n - 1;
i__1 = i__;
i__2 = i__;
if ((r__1 = d__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) >= (r__3 = dl[i__2].r, dabs(r__3)) + (r__4 =
r_imag(&dl[i__]), dabs(r__4))) {
i__1 = i__;
if ((r__1 = d__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) != 0.f) {
c_div(&q__1, &dl[i__], &d__[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__1 = i__;
dl[i__1].r = fact.r, dl[i__1].i = fact.i;
i__1 = i__ + 1;
i__2 = i__ + 1;
i__3 = i__;
q__2.r = fact.r * du[i__3].r - fact.i * du[i__3].i, q__2.i =
fact.r * du[i__3].i + fact.i * du[i__3].r;
q__1.r = d__[i__2].r - q__2.r, q__1.i = d__[i__2].i - q__2.i;
d__[i__1].r = q__1.r, d__[i__1].i = q__1.i;
}
} else {
c_div(&q__1, &d__[i__], &dl[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__1 = i__;
i__2 = i__;
d__[i__1].r = dl[i__2].r, d__[i__1].i = dl[i__2].i;
i__1 = i__;
dl[i__1].r = fact.r, dl[i__1].i = fact.i;
i__1 = i__;
temp.r = du[i__1].r, temp.i = du[i__1].i;
i__1 = i__;
i__2 = i__ + 1;
du[i__1].r = d__[i__2].r, du[i__1].i = d__[i__2].i;
i__1 = i__ + 1;
i__2 = i__ + 1;
q__2.r = fact.r * d__[i__2].r - fact.i * d__[i__2].i, q__2.i =
fact.r * d__[i__2].i + fact.i * d__[i__2].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
d__[i__1].r = q__1.r, d__[i__1].i = q__1.i;
ipiv[i__] = i__ + 1;
}
}
/* Check for a zero on the diagonal of U. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) == 0.f) {
*info = i__;
goto L50;
}
/* L40: */
}
L50:
return 0;
/* End of CGTTRF */
} /* cgttrf_ */
/* Subroutine */
int cla_syrfsx_extended_(integer *prec_type__, char *uplo, integer *n, integer *nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b, integer *ldb, complex *y, integer *ldy, real *berr_out__, integer * n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, complex *res, real *ayb, complex *dy, complex *y_tail__, real *rcond, integer * ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
real dxratmax, dzratmax;
integer i__, j;
logical incr_prec__;
extern /* Subroutine */
int cla_syamv_(integer *, integer *, real *, complex *, integer *, complex *, integer *, real *, real *, integer *);
real prev_dz_z__, yk, final_dx_x__;
extern /* Subroutine */
int cla_wwaddw_(integer *, complex *, complex *, complex *);
real final_dz_z__, prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__;
extern /* Subroutine */
int cla_lin_berr_(integer *, integer *, integer * , complex *, real *, real *);
real ymin;
integer y_prec_state__;
extern /* Subroutine */
int blas_csymv_x_(integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *, integer *);
integer uplo2;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int blas_csymv2_x_(integer *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, integer *), ccopy_(integer *, complex *, integer *, complex *, integer *);
real dxrat, dzrat;
extern /* Subroutine */
int caxpy_(integer *, complex *, complex *, integer *, complex *, integer *);
logical upper;
extern /* Subroutine */
int csymv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * );
real normx, normy;
extern real slamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *);
real normdx;
extern /* Subroutine */
int csytrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
real hugeval;
extern integer ilauplo_(char *);
integer x_state__, z_state__;
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*nrhs < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (*ldb < max(1,*n))
{
*info = -13;
}
else if (*ldy < max(1,*n))
{
*info = -15;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CLA_SYRFSX_EXTENDED", &i__1);
return 0;
}
eps = slamch_("Epsilon");
hugeval = slamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (real) (*n) * eps;
if (lsame_(uplo, "L"))
{
uplo2 = ilauplo_("L");
}
else
{
uplo2 = ilauplo_("U");
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
y_prec_state__ = 1;
if (y_prec_state__ == 2)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__;
y_tail__[i__3].r = 0.f;
y_tail__[i__3].i = 0.f; // , expr subst
}
}
dxrat = 0.f;
dxratmax = 0.f;
dzrat = 0.f;
dzratmax = 0.f;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1;
cnt <= i__2;
++cnt)
{
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0)
{
csymv_(uplo, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1);
}
else if (y_prec_state__ == 1)
{
blas_csymv_x_(&uplo2, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1, prec_type__);
}
else
{
blas_csymv2_x_(&uplo2, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b15, &res[1], & c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
ccopy_(n, &res[1], &c__1, &dy[1], &c__1);
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1], n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.f;
normy = 0.f;
normdx = 0.f;
dz_z__ = 0.f;
ymin = hugeval;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__ + j * y_dim1;
yk = (r__1 = y[i__4].r, f2c_abs(r__1)) + (r__2 = r_imag(&y[i__ + j * y_dim1]), f2c_abs(r__2));
i__4 = i__;
dyk = (r__1 = dy[i__4].r, f2c_abs(r__1)) + (r__2 = r_imag(&dy[i__] ), f2c_abs(r__2));
if (yk != 0.f)
{
/* Computing MAX */
r__1 = dz_z__;
r__2 = dyk / yk; // , expr subst
dz_z__ = max(r__1,r__2);
}
else if (dyk != 0.f)
{
dz_z__ = hugeval;
}
ymin = min(ymin,yk);
normy = max(normy,yk);
if (*colequ)
{
/* Computing MAX */
r__1 = normx;
r__2 = yk * c__[i__]; // , expr subst
normx = max(r__1,r__2);
/* Computing MAX */
r__1 = normdx;
r__2 = dyk * c__[i__]; // , expr subst
normdx = max(r__1,r__2);
}
else
{
normx = normy;
normdx = max(normdx,dyk);
}
}
if (normx != 0.f)
{
dx_x__ = normdx / normx;
}
else if (normdx == 0.f)
{
dx_x__ = 0.f;
}
else
{
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria. */
if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2)
{
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh)
{
x_state__ = 1;
}
if (x_state__ == 1)
{
if (dx_x__ <= eps)
{
x_state__ = 2;
}
else if (dxrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
x_state__ = 3;
}
}
else
{
if (dxrat > dxratmax)
{
dxratmax = dxrat;
}
}
if (x_state__ > 1)
{
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__)
{
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh)
{
z_state__ = 1;
}
if (z_state__ == 1)
{
if (dz_z__ <= eps)
{
z_state__ = 2;
}
else if (dz_z__ > *dz_ub__)
{
z_state__ = 0;
dzratmax = 0.f;
final_dz_z__ = hugeval;
}
else if (dzrat > *rthresh)
{
if (y_prec_state__ != 2)
{
incr_prec__ = TRUE_;
}
else
{
z_state__ = 3;
}
}
else
{
if (dzrat > dzratmax)
{
dzratmax = dzrat;
}
}
if (z_state__ > 1)
{
final_dz_z__ = dz_z__;
}
}
if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1))
{
goto L666;
}
if (incr_prec__)
{
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1;
i__ <= i__3;
++i__)
{
i__4 = i__;
y_tail__[i__4].r = 0.f;
y_tail__[i__4].i = 0.f; // , expr subst
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2)
{
caxpy_(n, &c_b15, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
}
else
{
cla_wwaddw_(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't CALL F90_EXIT. */
L666: /* Set final_* when cnt hits ithresh. */
if (x_state__ == 1)
{
final_dx_x__ = dx_x__;
}
if (z_state__ == 1)
{
final_dz_z__ = dz_z__;
}
/* Compute error bounds. */
if (*n_norms__ >= 1)
{
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 1 - dxratmax);
}
if (*n_norms__ >= 2)
{
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( f2c_abs(R(i)) / ( f2c_abs(op(A_s))*f2c_abs(Y) + f2c_abs(B_s) )(i) ) */
/* where f2c_abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
csymv_(uplo, n, &c_b14, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b15, &res[1], &c__1);
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
ayb[i__] = (r__1 = b[i__3].r, f2c_abs(r__1)) + (r__2 = r_imag(&b[i__ + j * b_dim1]), f2c_abs(r__2));
}
/* Compute f2c_abs(op(A_s))*f2c_abs(Y) + f2c_abs(B_s). */
cla_syamv_(&uplo2, n, &c_b37, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, &c_b37, &ayb[1], &c__1);
cla_lin_berr_(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
}
/* Subroutine */
int ctgevc_(char *side, char *howmny, logical *select, integer *n, complex *s, integer *lds, complex *p, integer *ldp, complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, integer *m, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4, r__5, r__6;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
complex d__;
integer i__, j;
complex ca, cb;
integer je, im, jr;
real big;
logical lsa, lsb;
real ulp;
complex sum;
integer ibeg, ieig, iend;
real dmin__;
integer isrc;
real temp;
complex suma, sumb;
real xmax, scale;
logical ilall;
integer iside;
real sbeta;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *);
real small;
logical compl;
real anorm, bnorm;
logical compr, ilbbad;
real acoefa, bcoefa, acoeff;
complex bcoeff;
logical ilback;
extern /* Subroutine */
int slabad_(real *, real *);
real ascale, bscale;
extern /* Complex */
VOID cladiv_(complex *, complex *, complex *);
extern real slamch_(char *);
complex salpha;
real safmin;
extern /* Subroutine */
int xerbla_(char *, integer *);
real bignum;
logical ilcomp;
integer ihwmny;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and Test the input parameters */
/* Parameter adjustments */
--select;
s_dim1 = *lds;
s_offset = 1 + s_dim1;
s -= s_offset;
p_dim1 = *ldp;
p_offset = 1 + p_dim1;
p -= p_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
if (lsame_(howmny, "A"))
{
ihwmny = 1;
ilall = TRUE_;
ilback = FALSE_;
}
else if (lsame_(howmny, "S"))
{
ihwmny = 2;
ilall = FALSE_;
ilback = FALSE_;
}
else if (lsame_(howmny, "B"))
{
ihwmny = 3;
ilall = TRUE_;
ilback = TRUE_;
}
else
{
ihwmny = -1;
}
if (lsame_(side, "R"))
{
iside = 1;
compl = FALSE_;
compr = TRUE_;
}
else if (lsame_(side, "L"))
{
iside = 2;
compl = TRUE_;
compr = FALSE_;
}
else if (lsame_(side, "B"))
{
iside = 3;
compl = TRUE_;
compr = TRUE_;
}
else
{
iside = -1;
}
*info = 0;
if (iside < 0)
{
*info = -1;
}
else if (ihwmny < 0)
{
*info = -2;
}
else if (*n < 0)
{
*info = -4;
}
else if (*lds < max(1,*n))
{
*info = -6;
}
else if (*ldp < max(1,*n))
{
*info = -8;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CTGEVC", &i__1);
return 0;
}
/* Count the number of eigenvectors */
if (! ilall)
{
im = 0;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
if (select[j])
{
++im;
}
/* L10: */
}
}
else
{
im = *n;
}
/* Check diagonal of B */
ilbbad = FALSE_;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
if (r_imag(&p[j + j * p_dim1]) != 0.f)
{
ilbbad = TRUE_;
}
/* L20: */
}
if (ilbbad)
{
*info = -7;
}
else if (compl && *ldvl < *n || *ldvl < 1)
{
*info = -10;
}
else if (compr && *ldvr < *n || *ldvr < 1)
{
*info = -12;
}
else if (*mm < im)
{
*info = -13;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CTGEVC", &i__1);
return 0;
}
/* Quick return if possible */
*m = im;
if (*n == 0)
{
return 0;
}
/* Machine Constants */
safmin = slamch_("Safe minimum");
big = 1.f / safmin;
slabad_(&safmin, &big);
ulp = slamch_("Epsilon") * slamch_("Base");
small = safmin * *n / ulp;
big = 1.f / small;
bignum = 1.f / (safmin * *n);
/* Compute the 1-norm of each column of the strictly upper triangular */
/* part of A and B to check for possible overflow in the triangular */
/* solver. */
i__1 = s_dim1 + 1;
anorm = (r__1 = s[i__1].r, abs(r__1)) + (r__2 = r_imag(&s[s_dim1 + 1]), abs(r__2));
i__1 = p_dim1 + 1;
bnorm = (r__1 = p[i__1].r, abs(r__1)) + (r__2 = r_imag(&p[p_dim1 + 1]), abs(r__2));
rwork[1] = 0.f;
rwork[*n + 1] = 0.f;
i__1 = *n;
for (j = 2;
j <= i__1;
++j)
{
rwork[j] = 0.f;
rwork[*n + j] = 0.f;
i__2 = j - 1;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * s_dim1;
rwork[j] += (r__1 = s[i__3].r, abs(r__1)) + (r__2 = r_imag(&s[i__ + j * s_dim1]), abs(r__2));
i__3 = i__ + j * p_dim1;
rwork[*n + j] += (r__1 = p[i__3].r, abs(r__1)) + (r__2 = r_imag(& p[i__ + j * p_dim1]), abs(r__2));
/* L30: */
}
/* Computing MAX */
i__2 = j + j * s_dim1;
r__3 = anorm;
r__4 = rwork[j] + ((r__1 = s[i__2].r, abs(r__1)) + ( r__2 = r_imag(&s[j + j * s_dim1]), abs(r__2))); // , expr subst
anorm = max(r__3,r__4);
/* Computing MAX */
i__2 = j + j * p_dim1;
r__3 = bnorm;
r__4 = rwork[*n + j] + ((r__1 = p[i__2].r, abs(r__1)) + (r__2 = r_imag(&p[j + j * p_dim1]), abs(r__2))); // , expr subst
bnorm = max(r__3,r__4);
/* L40: */
}
ascale = 1.f / max(anorm,safmin);
bscale = 1.f / max(bnorm,safmin);
/* Left eigenvectors */
if (compl)
{
ieig = 0;
/* Main loop over eigenvalues */
i__1 = *n;
for (je = 1;
je <= i__1;
++je)
{
if (ilall)
{
ilcomp = TRUE_;
}
else
{
ilcomp = select[je];
}
if (ilcomp)
{
++ieig;
i__2 = je + je * s_dim1;
i__3 = je + je * p_dim1;
if ((r__2 = s[i__2].r, abs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), abs(r__3)) <= safmin && (r__1 = p[i__3].r, abs(r__1)) <= safmin)
{
/* Singular matrix pencil -- return unit eigenvector */
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
i__3 = jr + ieig * vl_dim1;
vl[i__3].r = 0.f;
vl[i__3].i = 0.f; // , expr subst
/* L50: */
}
i__2 = ieig + ieig * vl_dim1;
vl[i__2].r = 1.f;
vl[i__2].i = 0.f; // , expr subst
goto L140;
}
/* Non-singular eigenvalue: */
/* Compute coefficients a and b in */
/* H */
/* y ( a A - b B ) = 0 */
/* Computing MAX */
i__2 = je + je * s_dim1;
i__3 = je + je * p_dim1;
r__4 = ((r__2 = s[i__2].r, abs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), abs(r__3))) * ascale;
r__5 = (r__1 = p[i__3].r, abs(r__1)) * bscale;
r__4 = max(r__4,r__5); // ; expr subst
temp = 1.f / max(r__4,safmin);
i__2 = je + je * s_dim1;
q__2.r = temp * s[i__2].r;
q__2.i = temp * s[i__2].i; // , expr subst
q__1.r = ascale * q__2.r;
q__1.i = ascale * q__2.i; // , expr subst
salpha.r = q__1.r;
salpha.i = q__1.i; // , expr subst
i__2 = je + je * p_dim1;
sbeta = temp * p[i__2].r * bscale;
acoeff = sbeta * ascale;
q__1.r = bscale * salpha.r;
q__1.i = bscale * salpha.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
/* Scale to avoid underflow */
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
lsb = (r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha), abs(r__2)) >= safmin && (r__3 = bcoeff.r, abs(r__3)) + (r__4 = r_imag(&bcoeff), abs(r__4)) < small;
scale = 1.f;
if (lsa)
{
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb)
{
/* Computing MAX */
r__3 = scale;
r__4 = small / ((r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha), abs(r__2))) * min( bnorm,big); // , expr subst
scale = max(r__3,r__4);
}
if (lsa || lsb)
{
/* Computing MIN */
/* Computing MAX */
r__5 = 1.f, r__6 = abs(acoeff);
r__5 = max(r__5,r__6);
r__6 = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(&bcoeff), abs(r__2)); // ; expr subst
r__3 = scale;
r__4 = 1.f / (safmin * max(r__5,r__6)); // , expr subst
scale = min(r__3,r__4);
if (lsa)
{
acoeff = ascale * (scale * sbeta);
}
else
{
acoeff = scale * acoeff;
}
if (lsb)
{
q__2.r = scale * salpha.r;
q__2.i = scale * salpha.i; // , expr subst
q__1.r = bscale * q__2.r;
q__1.i = bscale * q__2.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
}
else
{
q__1.r = scale * bcoeff.r;
q__1.i = scale * bcoeff.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
}
}
acoefa = abs(acoeff);
bcoefa = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(& bcoeff), abs(r__2));
xmax = 1.f;
i__2 = *n;
for (jr = 1;
jr <= i__2;
++jr)
{
i__3 = jr;
work[i__3].r = 0.f;
work[i__3].i = 0.f; // , expr subst
/* L60: */
}
i__2 = je;
work[i__2].r = 1.f;
work[i__2].i = 0.f; // , expr subst
/* Computing MAX */
r__1 = ulp * acoefa * anorm;
r__2 = ulp * bcoefa * bnorm;
r__1 = max(r__1,r__2); // ; expr subst
dmin__ = max(r__1,safmin);
/* H */
/* Triangular solve of (a A - b B) y = 0 */
/* H */
/* (rowwise in (a A - b B) , or columnwise in a A - b B) */
i__2 = *n;
for (j = je + 1;
j <= i__2;
++j)
{
/* Compute */
/* j-1 */
/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
/* k=je */
/* (Scale if necessary) */
temp = 1.f / xmax;
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum * temp)
{
i__3 = j - 1;
for (jr = je;
jr <= i__3;
++jr)
{
i__4 = jr;
i__5 = jr;
q__1.r = temp * work[i__5].r;
q__1.i = temp * work[i__5].i; // , expr subst
work[i__4].r = q__1.r;
work[i__4].i = q__1.i; // , expr subst
/* L70: */
}
xmax = 1.f;
}
suma.r = 0.f;
suma.i = 0.f; // , expr subst
sumb.r = 0.f;
sumb.i = 0.f; // , expr subst
i__3 = j - 1;
for (jr = je;
jr <= i__3;
++jr)
{
r_cnjg(&q__3, &s[jr + j * s_dim1]);
i__4 = jr;
q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4] .i;
q__2.i = q__3.r * work[i__4].i + q__3.i * work[i__4].r; // , expr subst
q__1.r = suma.r + q__2.r;
q__1.i = suma.i + q__2.i; // , expr subst
suma.r = q__1.r;
suma.i = q__1.i; // , expr subst
r_cnjg(&q__3, &p[jr + j * p_dim1]);
i__4 = jr;
q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4] .i;
q__2.i = q__3.r * work[i__4].i + q__3.i * work[i__4].r; // , expr subst
q__1.r = sumb.r + q__2.r;
q__1.i = sumb.i + q__2.i; // , expr subst
sumb.r = q__1.r;
sumb.i = q__1.i; // , expr subst
/* L80: */
}
q__2.r = acoeff * suma.r;
q__2.i = acoeff * suma.i; // , expr subst
r_cnjg(&q__4, &bcoeff);
q__3.r = q__4.r * sumb.r - q__4.i * sumb.i;
q__3.i = q__4.r * sumb.i + q__4.i * sumb.r; // , expr subst
q__1.r = q__2.r - q__3.r;
q__1.i = q__2.i - q__3.i; // , expr subst
sum.r = q__1.r;
sum.i = q__1.i; // , expr subst
/* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
/* with scaling and perturbation of the denominator */
i__3 = j + j * s_dim1;
q__3.r = acoeff * s[i__3].r;
q__3.i = acoeff * s[i__3].i; // , expr subst
i__4 = j + j * p_dim1;
q__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i;
q__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; // , expr subst
q__2.r = q__3.r - q__4.r;
q__2.i = q__3.i - q__4.i; // , expr subst
r_cnjg(&q__1, &q__2);
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs( r__2)) <= dmin__)
{
q__1.r = dmin__;
q__1.i = 0.f; // , expr subst
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
}
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs( r__2)) < 1.f)
{
if ((r__1 = sum.r, abs(r__1)) + (r__2 = r_imag(&sum), abs(r__2)) >= bignum * ((r__3 = d__.r, abs( r__3)) + (r__4 = r_imag(&d__), abs(r__4))))
{
temp = 1.f / ((r__1 = sum.r, abs(r__1)) + (r__2 = r_imag(&sum), abs(r__2)));
i__3 = j - 1;
for (jr = je;
jr <= i__3;
++jr)
{
i__4 = jr;
i__5 = jr;
q__1.r = temp * work[i__5].r;
q__1.i = temp * work[i__5].i; // , expr subst
work[i__4].r = q__1.r;
work[i__4].i = q__1.i; // , expr subst
/* L90: */
}
xmax = temp * xmax;
q__1.r = temp * sum.r;
q__1.i = temp * sum.i; // , expr subst
sum.r = q__1.r;
sum.i = q__1.i; // , expr subst
}
}
i__3 = j;
q__2.r = -sum.r;
q__2.i = -sum.i; // , expr subst
cladiv_(&q__1, &q__2, &d__);
work[i__3].r = q__1.r;
work[i__3].i = q__1.i; // , expr subst
/* Computing MAX */
i__3 = j;
r__3 = xmax;
r__4 = (r__1 = work[i__3].r, abs(r__1)) + ( r__2 = r_imag(&work[j]), abs(r__2)); // , expr subst
xmax = max(r__3,r__4);
/* L100: */
}
/* Back transform eigenvector if HOWMNY='B'. */
if (ilback)
{
i__2 = *n + 1 - je;
cgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl, &work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
isrc = 2;
ibeg = 1;
}
else
{
isrc = 1;
ibeg = je;
}
/* Copy and scale eigenvector into column of VL */
xmax = 0.f;
i__2 = *n;
for (jr = ibeg;
jr <= i__2;
++jr)
{
/* Computing MAX */
i__3 = (isrc - 1) * *n + jr;
r__3 = xmax;
r__4 = (r__1 = work[i__3].r, abs(r__1)) + ( r__2 = r_imag(&work[(isrc - 1) * *n + jr]), abs( r__2)); // , expr subst
xmax = max(r__3,r__4);
/* L110: */
}
if (xmax > safmin)
{
temp = 1.f / xmax;
i__2 = *n;
for (jr = ibeg;
jr <= i__2;
++jr)
{
i__3 = jr + ieig * vl_dim1;
i__4 = (isrc - 1) * *n + jr;
q__1.r = temp * work[i__4].r;
q__1.i = temp * work[ i__4].i; // , expr subst
vl[i__3].r = q__1.r;
vl[i__3].i = q__1.i; // , expr subst
/* L120: */
}
}
else
{
ibeg = *n + 1;
}
i__2 = ibeg - 1;
for (jr = 1;
jr <= i__2;
++jr)
{
i__3 = jr + ieig * vl_dim1;
vl[i__3].r = 0.f;
vl[i__3].i = 0.f; // , expr subst
/* L130: */
}
}
L140:
;
}
}
/* Right eigenvectors */
if (compr)
{
ieig = im + 1;
/* Main loop over eigenvalues */
for (je = *n;
je >= 1;
--je)
{
if (ilall)
{
ilcomp = TRUE_;
}
else
{
ilcomp = select[je];
}
if (ilcomp)
{
--ieig;
i__1 = je + je * s_dim1;
i__2 = je + je * p_dim1;
if ((r__2 = s[i__1].r, abs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), abs(r__3)) <= safmin && (r__1 = p[i__2].r, abs(r__1)) <= safmin)
{
/* Singular matrix pencil -- return unit eigenvector */
i__1 = *n;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr + ieig * vr_dim1;
vr[i__2].r = 0.f;
vr[i__2].i = 0.f; // , expr subst
/* L150: */
}
i__1 = ieig + ieig * vr_dim1;
vr[i__1].r = 1.f;
vr[i__1].i = 0.f; // , expr subst
goto L250;
}
/* Non-singular eigenvalue: */
/* Compute coefficients a and b in */
/* ( a A - b B ) x = 0 */
/* Computing MAX */
i__1 = je + je * s_dim1;
i__2 = je + je * p_dim1;
r__4 = ((r__2 = s[i__1].r, abs(r__2)) + (r__3 = r_imag(&s[je + je * s_dim1]), abs(r__3))) * ascale;
r__5 = (r__1 = p[i__2].r, abs(r__1)) * bscale;
r__4 = max(r__4,r__5); // ; expr subst
temp = 1.f / max(r__4,safmin);
i__1 = je + je * s_dim1;
q__2.r = temp * s[i__1].r;
q__2.i = temp * s[i__1].i; // , expr subst
q__1.r = ascale * q__2.r;
q__1.i = ascale * q__2.i; // , expr subst
salpha.r = q__1.r;
salpha.i = q__1.i; // , expr subst
i__1 = je + je * p_dim1;
sbeta = temp * p[i__1].r * bscale;
acoeff = sbeta * ascale;
q__1.r = bscale * salpha.r;
q__1.i = bscale * salpha.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
/* Scale to avoid underflow */
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
lsb = (r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha), abs(r__2)) >= safmin && (r__3 = bcoeff.r, abs(r__3)) + (r__4 = r_imag(&bcoeff), abs(r__4)) < small;
scale = 1.f;
if (lsa)
{
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb)
{
/* Computing MAX */
r__3 = scale;
r__4 = small / ((r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha), abs(r__2))) * min( bnorm,big); // , expr subst
scale = max(r__3,r__4);
}
if (lsa || lsb)
{
/* Computing MIN */
/* Computing MAX */
r__5 = 1.f, r__6 = abs(acoeff);
r__5 = max(r__5,r__6);
r__6 = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(&bcoeff), abs(r__2)); // ; expr subst
r__3 = scale;
r__4 = 1.f / (safmin * max(r__5,r__6)); // , expr subst
scale = min(r__3,r__4);
if (lsa)
{
acoeff = ascale * (scale * sbeta);
}
else
{
acoeff = scale * acoeff;
}
if (lsb)
{
q__2.r = scale * salpha.r;
q__2.i = scale * salpha.i; // , expr subst
q__1.r = bscale * q__2.r;
q__1.i = bscale * q__2.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
}
else
{
q__1.r = scale * bcoeff.r;
q__1.i = scale * bcoeff.i; // , expr subst
bcoeff.r = q__1.r;
bcoeff.i = q__1.i; // , expr subst
}
}
acoefa = abs(acoeff);
bcoefa = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(& bcoeff), abs(r__2));
xmax = 1.f;
i__1 = *n;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr;
work[i__2].r = 0.f;
work[i__2].i = 0.f; // , expr subst
/* L160: */
}
i__1 = je;
work[i__1].r = 1.f;
work[i__1].i = 0.f; // , expr subst
/* Computing MAX */
r__1 = ulp * acoefa * anorm;
r__2 = ulp * bcoefa * bnorm;
r__1 = max(r__1,r__2); // ; expr subst
dmin__ = max(r__1,safmin);
/* Triangular solve of (a A - b B) x = 0 (columnwise) */
/* WORK(1:j-1) contains sums w, */
/* WORK(j+1:JE) contains x */
i__1 = je - 1;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr;
i__3 = jr + je * s_dim1;
q__2.r = acoeff * s[i__3].r;
q__2.i = acoeff * s[i__3].i; // , expr subst
i__4 = jr + je * p_dim1;
q__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i;
q__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; // , expr subst
q__1.r = q__2.r - q__3.r;
q__1.i = q__2.i - q__3.i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
/* L170: */
}
i__1 = je;
work[i__1].r = 1.f;
work[i__1].i = 0.f; // , expr subst
for (j = je - 1;
j >= 1;
--j)
{
/* Form x(j) := - w(j) / d */
/* with scaling and perturbation of the denominator */
i__1 = j + j * s_dim1;
q__2.r = acoeff * s[i__1].r;
q__2.i = acoeff * s[i__1].i; // , expr subst
i__2 = j + j * p_dim1;
q__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i;
q__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2] .r; // , expr subst
q__1.r = q__2.r - q__3.r;
q__1.i = q__2.i - q__3.i; // , expr subst
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs( r__2)) <= dmin__)
{
q__1.r = dmin__;
q__1.i = 0.f; // , expr subst
d__.r = q__1.r;
d__.i = q__1.i; // , expr subst
}
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs( r__2)) < 1.f)
{
i__1 = j;
if ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag( &work[j]), abs(r__2)) >= bignum * ((r__3 = d__.r, abs(r__3)) + (r__4 = r_imag(&d__), abs( r__4))))
{
i__1 = j;
temp = 1.f / ((r__1 = work[i__1].r, abs(r__1)) + ( r__2 = r_imag(&work[j]), abs(r__2)));
i__1 = je;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr;
i__3 = jr;
q__1.r = temp * work[i__3].r;
q__1.i = temp * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
/* L180: */
}
}
}
i__1 = j;
i__2 = j;
q__2.r = -work[i__2].r;
q__2.i = -work[i__2].i; // , expr subst
cladiv_(&q__1, &q__2, &d__);
work[i__1].r = q__1.r;
work[i__1].i = q__1.i; // , expr subst
if (j > 1)
{
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
i__1 = j;
if ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag( &work[j]), abs(r__2)) > 1.f)
{
i__1 = j;
temp = 1.f / ((r__1 = work[i__1].r, abs(r__1)) + ( r__2 = r_imag(&work[j]), abs(r__2)));
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >= bignum * temp)
{
i__1 = je;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr;
i__3 = jr;
q__1.r = temp * work[i__3].r;
q__1.i = temp * work[i__3].i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
/* L190: */
}
}
}
i__1 = j;
q__1.r = acoeff * work[i__1].r;
q__1.i = acoeff * work[i__1].i; // , expr subst
ca.r = q__1.r;
ca.i = q__1.i; // , expr subst
i__1 = j;
q__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[ i__1].i;
q__1.i = bcoeff.r * work[i__1].i + bcoeff.i * work[i__1].r; // , expr subst
cb.r = q__1.r;
cb.i = q__1.i; // , expr subst
i__1 = j - 1;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr;
i__3 = jr;
i__4 = jr + j * s_dim1;
q__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i;
q__3.i = ca.r * s[i__4].i + ca.i * s[i__4] .r; // , expr subst
q__2.r = work[i__3].r + q__3.r;
q__2.i = work[ i__3].i + q__3.i; // , expr subst
i__5 = jr + j * p_dim1;
q__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i;
q__4.i = cb.r * p[i__5].i + cb.i * p[i__5] .r; // , expr subst
q__1.r = q__2.r - q__4.r;
q__1.i = q__2.i - q__4.i; // , expr subst
work[i__2].r = q__1.r;
work[i__2].i = q__1.i; // , expr subst
/* L200: */
}
}
/* L210: */
}
/* Back transform eigenvector if HOWMNY='B'. */
if (ilback)
{
cgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
isrc = 2;
iend = *n;
}
else
{
isrc = 1;
iend = je;
}
/* Copy and scale eigenvector into column of VR */
xmax = 0.f;
i__1 = iend;
for (jr = 1;
jr <= i__1;
++jr)
{
/* Computing MAX */
i__2 = (isrc - 1) * *n + jr;
r__3 = xmax;
r__4 = (r__1 = work[i__2].r, abs(r__1)) + ( r__2 = r_imag(&work[(isrc - 1) * *n + jr]), abs( r__2)); // , expr subst
xmax = max(r__3,r__4);
/* L220: */
}
if (xmax > safmin)
{
temp = 1.f / xmax;
i__1 = iend;
for (jr = 1;
jr <= i__1;
++jr)
{
i__2 = jr + ieig * vr_dim1;
i__3 = (isrc - 1) * *n + jr;
q__1.r = temp * work[i__3].r;
q__1.i = temp * work[ i__3].i; // , expr subst
vr[i__2].r = q__1.r;
vr[i__2].i = q__1.i; // , expr subst
/* L230: */
}
}
else
{
iend = 0;
}
i__1 = *n;
for (jr = iend + 1;
jr <= i__1;
++jr)
{
i__2 = jr + ieig * vr_dim1;
vr[i__2].r = 0.f;
vr[i__2].i = 0.f; // , expr subst
/* L240: */
}
}
L250:
;
}
}
return 0;
/* End of CTGEVC */
}
/* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, integer *n, complex *a, integer *lda, complex *w, complex *vl,
integer *ldvl, complex *vr, integer *ldvr, integer *ilo, integer *ihi,
real *scale, real *abnrm, real *rconde, real *rcondv, complex *work,
integer *lwork, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
real r__1, r__2;
complex q__1, q__2;
/* Local variables */
integer i__, k;
char job[1];
real scl, dum[1], eps;
complex tmp;
char side[1];
real anrm;
integer ierr, itau, iwrk, nout;
integer icond;
logical scalea;
real cscale;
logical select[1];
real bignum;
integer minwrk, maxwrk;
logical wantvl, wntsnb;
integer hswork;
logical wntsne;
real smlnum;
logical lquery, wantvr, wntsnn, wntsnv;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* Optionally also, it computes a balancing transformation to improve */
/* the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */
/* (RCONDE), and reciprocal condition numbers for the right */
/* eigenvectors (RCONDV). */
/* The right eigenvector v(j) of A satisfies */
/* A * v(j) = lambda(j) * v(j) */
/* where lambda(j) is its eigenvalue. */
/* The left eigenvector u(j) of A satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component real. */
/* Balancing a matrix means permuting the rows and columns to make it */
/* more nearly upper triangular, and applying a diagonal similarity */
/* transformation D * A * D**(-1), where D is a diagonal matrix, to */
/* make its rows and columns closer in norm and the condition numbers */
/* of its eigenvalues and eigenvectors smaller. The computed */
/* reciprocal condition numbers correspond to the balanced matrix. */
/* Permuting rows and columns will not change the condition numbers */
/* (in exact arithmetic) but diagonal scaling will. For further */
/* explanation of balancing, see section 4.10.2 of the LAPACK */
/* Users' Guide. */
/* Arguments */
/* ========= */
/* BALANC (input) CHARACTER*1 */
/* Indicates how the input matrix should be diagonally scaled */
/* and/or permuted to improve the conditioning of its */
/* eigenvalues. */
/* = 'N': Do not diagonally scale or permute; */
/* = 'P': Perform permutations to make the matrix more nearly */
/* upper triangular. Do not diagonally scale; */
/* = 'S': Diagonally scale the matrix, ie. replace A by */
/* D*A*D**(-1), where D is a diagonal matrix chosen */
/* to make the rows and columns of A more equal in */
/* norm. Do not permute; */
/* = 'B': Both diagonally scale and permute A. */
/* Computed reciprocal condition numbers will be for the matrix */
/* after balancing and/or permuting. Permuting does not change */
/* condition numbers (in exact arithmetic), but balancing does. */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVL must = 'V'. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVR must = 'V'. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N': None are computed; */
/* = 'E': Computed for eigenvalues only; */
/* = 'V': Computed for right eigenvectors only; */
/* = 'B': Computed for eigenvalues and right eigenvectors. */
/* If SENSE = 'E' or 'B', both left and right eigenvectors */
/* must also be computed (JOBVL = 'V' and JOBVR = 'V'). */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. If JOBVL = 'V' or */
/* JOBVR = 'V', A contains the Schur form of the balanced */
/* version of the matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* W (output) COMPLEX array, dimension (N) */
/* W contains the computed eigenvalues. */
/* VL (output) COMPLEX array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order */
/* as their eigenvalues. */
/* If JOBVL = 'N', VL is not referenced. */
/* u(j) = VL(:,j), the j-th column of VL. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order */
/* as their eigenvalues. */
/* If JOBVR = 'N', VR is not referenced. */
/* v(j) = VR(:,j), the j-th column of VR. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are integer values determined when A was */
/* balanced. The balanced A(i,j) = 0 if I > J and */
/* SCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* when balancing A. If P(j) is the index of the row and column */
/* interchanged with row and column j, and D(j) is the scaling */
/* factor applied to row and column j, then */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* ABNRM (output) REAL */
/* The one-norm of the balanced matrix (the maximum */
/* of the sum of absolute values of elements of any column). */
/* RCONDE (output) REAL array, dimension (N) */
/* RCONDE(j) is the reciprocal condition number of the j-th */
/* eigenvalue. */
/* RCONDV (output) REAL array, dimension (N) */
/* RCONDV(j) is the reciprocal condition number of the j-th */
/* right eigenvector. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. If SENSE = 'N' or 'E', */
/* LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', */
/* LWORK >= N*N+2*N. */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, the QR algorithm failed to compute all the */
/* eigenvalues, and no eigenvectors or condition numbers */
/* have been computed; elements 1:ILO-1 and i+1:N of W */
/* contain eigenvalues which have converged. */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--scale;
--rconde;
--rcondv;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
wntsnn = lsame_(sense, "N");
wntsne = lsame_(sense, "E");
wntsnv = lsame_(sense, "V");
wntsnb = lsame_(sense, "B");
if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P")
|| lsame_(balanc, "B"))) {
*info = -1;
} else if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -2;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -3;
} else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
&& ! (wantvl && wantvr)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -10;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -12;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to real */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by CHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0);
if (wantvl) {
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
} else {
if (wntsnn) {
chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
} else {
chseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
}
}
hswork = work[1].r;
if (! wantvl && ! wantvr) {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
} else {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 1;
maxwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,minwrk);
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEEVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
cgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = clange_("1", n, n, &a[a_offset], lda, dum);
if (scalea) {
dum[0] = *abnrm;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
ierr);
*abnrm = dum[0];
}
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
ierr);
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* If condition numbers desired, compute Schur form */
if (wntsnn) {
*(unsigned char *)job = 'E';
} else {
*(unsigned char *)job = 'S';
}
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need N) */
ctrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], &
ierr);
}
/* Compute condition numbers if desired */
/* (CWorkspace: need N*N+2*N unless SENSE = 'E') */
/* (RWorkspace: need 2*N unless SENSE = 'E') */
if (! wntsnn) {
ctrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout,
&work[iwrk], n, &rwork[1], &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
cgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
r__1 = vl[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vl[k + i__ * vl_dim1]);
rwork[k] = r__1 * r__1 + r__2 * r__2;
}
k = isamax_(n, &rwork[1], &c__1);
r_cnjg(&q__2, &vl[k + i__ * vl_dim1]);
r__1 = sqrt(rwork[k]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
r__1 = vl[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vl[i__2].r = q__1.r, vl[i__2].i = q__1.i;
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
cgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
r__1 = vr[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vr[k + i__ * vr_dim1]);
rwork[k] = r__1 * r__1 + r__2 * r__2;
}
k = isamax_(n, &rwork[1], &c__1);
r_cnjg(&q__2, &vr[k + i__ * vr_dim1]);
r__1 = sqrt(rwork[k]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
r__1 = vr[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info == 0) {
if ((wntsnv || wntsnb) && icond == 0) {
slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
1], n, &ierr);
}
} else {
i__1 = *ilo - 1;
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEEVX */
} /* cgeevx_ */
/* Subroutine */ int cgbt05_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, complex *ab, integer *ldab, complex *b, integer *
ldb, complex *x, integer *ldx, complex *xact, integer *ldxact, real *
ferr, real *berr, real *reslts)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, xact_dim1,
xact_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1, q__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static real diff, axbi;
static integer imax;
static real unfl, ovfl;
static integer i__, j, k;
extern logical lsame_(char *, char *);
static real xnorm;
extern integer icamax_(integer *, complex *, integer *);
extern doublereal slamch_(char *);
static integer nz;
static real errbnd;
static logical notran;
static real eps, tmp;
#define xact_subscr(a_1,a_2) (a_2)*xact_dim1 + a_1
#define xact_ref(a_1,a_2) xact[xact_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
#define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1
#define ab_ref(a_1,a_2) ab[ab_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
CGBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations op(A)*X = B, where A is a
general band matrix of order n with kl subdiagonals and ku
superdiagonals and op(A) = A or A**T, depending on TRANS.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS (input) INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AB (input) COMPLEX array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input) COMPLEX array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT (input) COMPLEX array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT (input) INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR (input) REAL array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR (input) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS (output) REAL array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
=====================================================================
Quick exit if N = 0 or NRHS = 0.
Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
xact_dim1 = *ldxact;
xact_offset = 1 + xact_dim1 * 1;
xact -= xact_offset;
--ferr;
--berr;
--reslts;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
reslts[1] = 0.f;
reslts[2] = 0.f;
return 0;
}
eps = slamch_("Epsilon");
unfl = slamch_("Safe minimum");
ovfl = 1.f / unfl;
notran = lsame_(trans, "N");
/* Computing MIN */
i__1 = *kl + *ku + 2, i__2 = *n + 1;
nz = min(i__1,i__2);
/* Test 1: Compute the maximum of
norm(X - XACT) / ( norm(X) * FERR )
over all the vectors X and XACT using the infinity-norm. */
errbnd = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
imax = icamax_(n, &x_ref(1, j), &c__1);
/* Computing MAX */
i__2 = x_subscr(imax, j);
r__3 = (r__1 = x[i__2].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(imax, j)
), dabs(r__2));
xnorm = dmax(r__3,unfl);
diff = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = x_subscr(i__, j);
i__4 = xact_subscr(i__, j);
q__2.r = x[i__3].r - xact[i__4].r, q__2.i = x[i__3].i - xact[i__4]
.i;
q__1.r = q__2.r, q__1.i = q__2.i;
/* Computing MAX */
r__3 = diff, r__4 = (r__1 = q__1.r, dabs(r__1)) + (r__2 = r_imag(&
q__1), dabs(r__2));
diff = dmax(r__3,r__4);
/* L10: */
}
if (xnorm > 1.f) {
goto L20;
} else if (diff <= ovfl * xnorm) {
goto L20;
} else {
errbnd = 1.f / eps;
goto L30;
}
L20:
if (diff / xnorm <= ferr[j]) {
/* Computing MAX */
r__1 = errbnd, r__2 = diff / xnorm / ferr[j];
errbnd = dmax(r__1,r__2);
} else {
errbnd = 1.f / eps;
}
L30:
;
}
reslts[1] = errbnd;
/* Test 2: Compute the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) */
i__1 = *nrhs;
for (k = 1; k <= i__1; ++k) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, k);
tmp = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(i__,
k)), dabs(r__2));
if (notran) {
/* Computing MAX */
i__3 = i__ - *kl;
/* Computing MIN */
i__5 = i__ + *ku;
i__4 = min(i__5,*n);
for (j = max(i__3,1); j <= i__4; ++j) {
i__3 = ab_subscr(*ku + 1 + i__ - j, j);
i__5 = x_subscr(j, k);
tmp += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
ab_ref(*ku + 1 + i__ - j, j)), dabs(r__2))) * ((
r__3 = x[i__5].r, dabs(r__3)) + (r__4 = r_imag(&
x_ref(j, k)), dabs(r__4)));
/* L40: */
}
} else {
/* Computing MAX */
i__4 = i__ - *ku;
/* Computing MIN */
i__5 = i__ + *kl;
i__3 = min(i__5,*n);
for (j = max(i__4,1); j <= i__3; ++j) {
i__4 = ab_subscr(*ku + 1 + j - i__, i__);
i__5 = x_subscr(j, k);
tmp += ((r__1 = ab[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
ab_ref(*ku + 1 + j - i__, i__)), dabs(r__2))) * ((
r__3 = x[i__5].r, dabs(r__3)) + (r__4 = r_imag(&
x_ref(j, k)), dabs(r__4)));
/* L50: */
}
}
if (i__ == 1) {
axbi = tmp;
} else {
axbi = dmin(axbi,tmp);
}
/* L60: */
}
/* Computing MAX */
r__1 = axbi, r__2 = nz * unfl;
tmp = berr[k] / (nz * eps + nz * unfl / dmax(r__1,r__2));
if (k == 1) {
reslts[2] = tmp;
} else {
reslts[2] = dmax(reslts[2],tmp);
}
/* L70: */
}
return 0;
/* End of CGBT05 */
} /* cgbt05_ */
/* Subroutine */ int cla_gbamv__(integer *trans, integer *m, integer *n,
integer *kl, integer *ku, real *alpha, complex *ab, integer *ldab,
complex *x, integer *incx, real *beta, real *y, integer *incy)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *), r_sign(real *, real *);
/* Local variables */
extern integer ilatrans_(char *);
integer i__, j;
logical symb_zero__;
integer kd, iy, jx, kx, ky, info;
real temp;
integer lenx, leny;
real safe1;
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLA_GEAMV performs one of the matrix-vector operations */
/* y := alpha*abs(A)*abs(x) + beta*abs(y), */
/* or y := alpha*abs(A)'*abs(x) + beta*abs(y), */
/* where alpha and beta are scalars, x and y are vectors and A is an */
/* m by n matrix. */
/* This function is primarily used in calculating error bounds. */
/* To protect against underflow during evaluation, components in */
/* the resulting vector are perturbed away from zero by (N+1) */
/* times the underflow threshold. To prevent unnecessarily large */
/* errors for block-structure embedded in general matrices, */
/* "symbolically" zero components are not perturbed. A zero */
/* entry is considered "symbolic" if all multiplications involved */
/* in computing that entry have at least one zero multiplicand. */
/* Parameters */
/* ========== */
/* TRANS - INTEGER */
/* On entry, TRANS specifies the operation to be performed as */
/* follows: */
/* BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) */
/* BLAS_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y) */
/* BLAS_CONJ_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y) */
/* Unchanged on exit. */
/* M - INTEGER */
/* On entry, M specifies the number of rows of the matrix A. */
/* M must be at least zero. */
/* Unchanged on exit. */
/* N - INTEGER */
/* On entry, N specifies the number of columns of the matrix A. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* KL - INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU - INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* ALPHA - REAL */
/* On entry, ALPHA specifies the scalar alpha. */
/* Unchanged on exit. */
/* A - REAL array of DIMENSION ( LDA, n ) */
/* Before entry, the leading m by n part of the array A must */
/* contain the matrix of coefficients. */
/* Unchanged on exit. */
/* LDA - INTEGER */
/* On entry, LDA specifies the first dimension of A as declared */
/* in the calling (sub) program. LDA must be at least */
/* max( 1, m ). */
/* Unchanged on exit. */
/* X - REAL array of DIMENSION at least */
/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
/* Before entry, the incremented array X must contain the */
/* vector x. */
/* Unchanged on exit. */
/* INCX - INTEGER */
/* On entry, INCX specifies the increment for the elements of */
/* X. INCX must not be zero. */
/* Unchanged on exit. */
/* BETA - REAL */
/* On entry, BETA specifies the scalar beta. When BETA is */
/* supplied as zero then Y need not be set on input. */
/* Unchanged on exit. */
/* Y - REAL array of DIMENSION at least */
/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
/* Before entry with BETA non-zero, the incremented array Y */
/* must contain the vector y. On exit, Y is overwritten by the */
/* updated vector y. */
/* INCY - INTEGER */
/* On entry, INCY specifies the increment for the elements of */
/* Y. INCY must not be zero. */
/* Unchanged on exit. */
/* Level 2 Blas routine. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! (*trans == ilatrans_("N") || *trans == ilatrans_("T") || *trans == ilatrans_("C"))) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*kl < 0) {
info = 4;
} else if (*ku < 0) {
info = 5;
} else if (*ldab < *kl + *ku + 1) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("CLA_GBAMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.f && *beta == 1.f) {
return 0;
}
/* Set LENX and LENY, the lengths of the vectors x and y, and set */
/* up the start points in X and Y. */
if (*trans == ilatrans_("N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/* Set SAFE1 essentially to be the underflow threshold times the */
/* number of additions in each row. */
safe1 = slamch_("Safe minimum");
safe1 = (*n + 1) * safe1;
/* Form y := alpha*abs(A)*abs(x) + beta*abs(y). */
/* The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to */
/* the inexact flag. Still doesn't help change the iteration order */
/* to per-column. */
kd = *ku + 1;
iy = ky;
if (*incx == 1) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
if (*beta == 0.f) {
symb_zero__ = TRUE_;
y[iy] = 0.f;
} else if (y[iy] == 0.f) {
symb_zero__ = TRUE_;
} else {
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], dabs(r__1));
}
if (*alpha != 0.f) {
/* Computing MAX */
i__2 = i__ - *ku;
/* Computing MIN */
i__4 = i__ + *kl;
i__3 = min(i__4,lenx);
for (j = max(i__2,1); j <= i__3; ++j) {
if (*trans == ilatrans_("N")) {
i__2 = kd + i__ - j + j * ab_dim1;
temp = (r__1 = ab[i__2].r, dabs(r__1)) + (r__2 =
r_imag(&ab[kd + i__ - j + j * ab_dim1]), dabs(
r__2));
} else {
i__2 = j + (kd + i__ - j) * ab_dim1;
temp = (r__1 = ab[i__2].r, dabs(r__1)) + (r__2 =
r_imag(&ab[j + (kd + i__ - j) * ab_dim1]),
dabs(r__2));
}
i__2 = j;
symb_zero__ = symb_zero__ && (x[i__2].r == 0.f && x[i__2]
.i == 0.f || temp == 0.f);
i__2 = j;
y[iy] += *alpha * ((r__1 = x[i__2].r, dabs(r__1)) + (r__2
= r_imag(&x[j]), dabs(r__2))) * temp;
}
}
if (! symb_zero__) {
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
if (*beta == 0.f) {
symb_zero__ = TRUE_;
y[iy] = 0.f;
} else if (y[iy] == 0.f) {
symb_zero__ = TRUE_;
} else {
symb_zero__ = FALSE_;
y[iy] = *beta * (r__1 = y[iy], dabs(r__1));
}
if (*alpha != 0.f) {
jx = kx;
/* Computing MAX */
i__3 = i__ - *ku;
/* Computing MIN */
i__4 = i__ + *kl;
i__2 = min(i__4,lenx);
for (j = max(i__3,1); j <= i__2; ++j) {
if (*trans == ilatrans_("N")) {
i__3 = kd + i__ - j + j * ab_dim1;
temp = (r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[kd + i__ - j + j * ab_dim1]), dabs(
r__2));
} else {
i__3 = j + (kd + i__ - j) * ab_dim1;
temp = (r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[j + (kd + i__ - j) * ab_dim1]),
dabs(r__2));
}
i__3 = jx;
symb_zero__ = symb_zero__ && (x[i__3].r == 0.f && x[i__3]
.i == 0.f || temp == 0.f);
i__3 = jx;
y[iy] += *alpha * ((r__1 = x[i__3].r, dabs(r__1)) + (r__2
= r_imag(&x[jx]), dabs(r__2))) * temp;
jx += *incx;
}
}
if (! symb_zero__) {
y[iy] += r_sign(&safe1, &y[iy]);
}
iy += *incy;
}
}
return 0;
/* End of CLA_GBAMV */
} /* cla_gbamv__ */
/* DECK CSIDI */
/* Subroutine */ int csidi_(complex *a, integer *lda, integer *n, integer *
kpvt, complex *det, complex *work, integer *job)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
static complex d__;
static integer j, k;
static complex t, ak;
static integer jb, ks, km1;
static real ten;
static complex akp1, temp, akkp1;
static logical nodet;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
extern /* Complex */ void cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer kstep;
static logical noinv;
/* ***BEGIN PROLOGUE CSIDI */
/* ***PURPOSE Compute the determinant and inverse of a complex symmetric */
/* matrix using the factors from CSIFA. */
/* ***LIBRARY SLATEC (LINPACK) */
/* ***CATEGORY D2C1, D3C1 */
/* ***TYPE COMPLEX (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C) */
/* ***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, */
/* SYMMETRIC */
/* ***AUTHOR Bunch, J., (UCSD) */
/* ***DESCRIPTION */
/* CSIDI computes the determinant and inverse */
/* of a complex symmetric matrix using the factors from CSIFA. */
/* On Entry */
/* A COMPLEX(LDA,N) */
/* the output from CSIFA. */
/* LDA INTEGER */
/* the leading dimension of the array A . */
/* N INTEGER */
/* the order of the matrix A . */
/* KVPT INTEGER(N) */
/* the pivot vector from CSIFA. */
/* WORK COMPLEX(N) */
/* work vector. Contents destroyed. */
/* JOB INTEGER */
/* JOB has the decimal expansion AB where */
/* If B .NE. 0, the inverse is computed, */
/* If A .NE. 0, the determinant is computed, */
/* For example, JOB = 11 gives both. */
/* On Return */
/* Variables not requested by JOB are not used. */
/* A contains the upper triangle of the inverse of */
/* the original matrix. The strict lower triangle */
/* is never referenced. */
/* DET COMPLEX(2) */
/* determinant of original matrix. */
/* Determinant = DET(1) * 10.0**DET(2) */
/* with 1.0 .LE. ABS(DET(1)) .LT. 10.0 */
/* or DET(1) = 0.0. */
/* Error Condition */
/* A division by zero may occur if the inverse is requested */
/* and CSICO has set RCOND .EQ. 0.0 */
/* or CSIFA has set INFO .NE. 0 . */
/* ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. */
/* Stewart, LINPACK Users' Guide, SIAM, 1979. */
/* ***ROUTINES CALLED CAXPY, CCOPY, CDOTU, CSWAP */
/* ***REVISION HISTORY (YYMMDD) */
/* 780814 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890831 Modified array declarations. (WRB) */
/* 891107 Corrected category and modified routine equivalence */
/* list. (WRB) */
/* 891107 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900326 Removed duplicate information from DESCRIPTION section. */
/* (WRB) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* ***END PROLOGUE CSIDI */
/* ***FIRST EXECUTABLE STATEMENT CSIDI */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--kpvt;
--det;
--work;
/* Function Body */
noinv = *job % 10 == 0;
nodet = *job % 100 / 10 == 0;
if (nodet) {
goto L100;
}
det[1].r = 1.f, det[1].i = 0.f;
det[2].r = 0.f, det[2].i = 0.f;
ten = 10.f;
t.r = 0.f, t.i = 0.f;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k + k * a_dim1;
d__.r = a[i__2].r, d__.i = a[i__2].i;
/* CHECK IF 1 BY 1 */
if (kpvt[k] > 0) {
goto L30;
}
/* 2 BY 2 BLOCK */
/* USE DET (D T) = (D/T * C - T) * T */
/* (T C) */
/* TO AVOID UNDERFLOW/OVERFLOW TROUBLES. */
/* TAKE TWO PASSES THROUGH SCALING. USE T FOR FLAG. */
if ((r__1 = t.r, dabs(r__1)) + (r__2 = r_imag(&t), dabs(r__2)) != 0.f)
{
goto L10;
}
i__2 = k + (k + 1) * a_dim1;
t.r = a[i__2].r, t.i = a[i__2].i;
c_div(&q__3, &d__, &t);
i__2 = k + 1 + (k + 1) * a_dim1;
q__2.r = q__3.r * a[i__2].r - q__3.i * a[i__2].i, q__2.i = q__3.r * a[
i__2].i + q__3.i * a[i__2].r;
q__1.r = q__2.r - t.r, q__1.i = q__2.i - t.i;
d__.r = q__1.r, d__.i = q__1.i;
goto L20;
L10:
d__.r = t.r, d__.i = t.i;
t.r = 0.f, t.i = 0.f;
L20:
L30:
q__1.r = d__.r * det[1].r - d__.i * det[1].i, q__1.i = d__.r * det[1]
.i + d__.i * det[1].r;
det[1].r = q__1.r, det[1].i = q__1.i;
if ((r__1 = det[1].r, dabs(r__1)) + (r__2 = r_imag(&det[1]), dabs(
r__2)) == 0.f) {
goto L80;
}
L40:
if ((r__1 = det[1].r, dabs(r__1)) + (r__2 = r_imag(&det[1]), dabs(
r__2)) >= 1.f) {
goto L50;
}
q__2.r = ten, q__2.i = 0.f;
q__1.r = q__2.r * det[1].r - q__2.i * det[1].i, q__1.i = q__2.r * det[
1].i + q__2.i * det[1].r;
det[1].r = q__1.r, det[1].i = q__1.i;
q__1.r = det[2].r - 1.f, q__1.i = det[2].i - 0.f;
det[2].r = q__1.r, det[2].i = q__1.i;
goto L40;
L50:
L60:
if ((r__1 = det[1].r, dabs(r__1)) + (r__2 = r_imag(&det[1]), dabs(
r__2)) < ten) {
goto L70;
}
q__2.r = ten, q__2.i = 0.f;
c_div(&q__1, &det[1], &q__2);
det[1].r = q__1.r, det[1].i = q__1.i;
q__1.r = det[2].r + 1.f, q__1.i = det[2].i + 0.f;
det[2].r = q__1.r, det[2].i = q__1.i;
goto L60;
L70:
L80:
/* L90: */
;
}
L100:
/* COMPUTE INVERSE(A) */
if (noinv) {
goto L230;
}
k = 1;
L110:
if (k > *n) {
goto L220;
}
km1 = k - 1;
if (kpvt[k] < 0) {
goto L140;
}
/* 1 BY 1 */
i__1 = k + k * a_dim1;
c_div(&q__1, &c_b3, &a[k + k * a_dim1]);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
if (km1 < 1) {
goto L130;
}
ccopy_(&km1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = km1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
cdotu_(&q__1, &j, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = j - 1;
caxpy_(&i__2, &work[j], &a[j * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1],
&c__1);
/* L120: */
}
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
cdotu_(&q__2, &km1, &work[1], &c__1, &a[k * a_dim1 + 1], &c__1);
q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
L130:
kstep = 1;
goto L180;
L140:
/* 2 BY 2 */
i__1 = k + (k + 1) * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
c_div(&q__1, &a[k + k * a_dim1], &t);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &a[k + 1 + (k + 1) * a_dim1], &t);
akp1.r = q__1.r, akp1.i = q__1.i;
c_div(&q__1, &a[k + (k + 1) * a_dim1], &t);
akkp1.r = q__1.r, akkp1.i = q__1.i;
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i + ak.i *
akp1.r;
q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i *
q__2.r;
d__.r = q__1.r, d__.i = q__1.i;
i__1 = k + k * a_dim1;
c_div(&q__1, &akp1, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = k + 1 + (k + 1) * a_dim1;
c_div(&q__1, &ak, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = k + (k + 1) * a_dim1;
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
c_div(&q__1, &q__2, &d__);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
if (km1 < 1) {
goto L170;
}
ccopy_(&km1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = km1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + (k + 1) * a_dim1;
cdotu_(&q__1, &j, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = j - 1;
caxpy_(&i__2, &work[j], &a[j * a_dim1 + 1], &c__1, &a[(k + 1) *
a_dim1 + 1], &c__1);
/* L150: */
}
i__1 = k + 1 + (k + 1) * a_dim1;
i__2 = k + 1 + (k + 1) * a_dim1;
cdotu_(&q__2, &km1, &work[1], &c__1, &a[(k + 1) * a_dim1 + 1], &c__1);
q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = k + (k + 1) * a_dim1;
i__2 = k + (k + 1) * a_dim1;
cdotu_(&q__2, &km1, &a[k * a_dim1 + 1], &c__1, &a[(k + 1) * a_dim1 + 1], &
c__1);
q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
ccopy_(&km1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = km1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
cdotu_(&q__1, &j, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = j - 1;
caxpy_(&i__2, &work[j], &a[j * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1],
&c__1);
/* L160: */
}
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
cdotu_(&q__2, &km1, &work[1], &c__1, &a[k * a_dim1 + 1], &c__1);
q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
L170:
kstep = 2;
L180:
/* SWAP */
ks = (i__1 = kpvt[k], abs(i__1));
if (ks == k) {
goto L210;
}
cswap_(&ks, &a[ks * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
i__1 = k;
for (jb = ks; jb <= i__1; ++jb) {
j = k + ks - jb;
i__2 = j + k * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
i__2 = j + k * a_dim1;
i__3 = ks + j * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
i__2 = ks + j * a_dim1;
a[i__2].r = temp.r, a[i__2].i = temp.i;
/* L190: */
}
if (kstep == 1) {
goto L200;
}
i__1 = ks + (k + 1) * a_dim1;
temp.r = a[i__1].r, temp.i = a[i__1].i;
i__1 = ks + (k + 1) * a_dim1;
i__2 = k + (k + 1) * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = k + (k + 1) * a_dim1;
a[i__1].r = temp.r, a[i__1].i = temp.i;
L200:
L210:
k += kstep;
goto L110;
L220:
L230:
return 0;
} /* csidi_ */
int cgeev_(char *jobvl, char *jobvr, int *n, complex *a,
int *lda, complex *w, complex *vl, int *ldvl, complex *vr,
int *ldvr, complex *work, int *lwork, float *rwork, int *
info)
{
/* System generated locals */
int a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
float r__1, r__2;
complex q__1, q__2;
/* Builtin functions */
double sqrt(double), r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
int i__, k, ihi;
float scl;
int ilo;
float dum[1], eps;
complex tmp;
int ibal;
char side[1];
float anrm;
int ierr, itau, iwrk, nout;
extern int cscal_(int *, complex *, complex *,
int *);
extern int lsame_(char *, char *);
extern double scnrm2_(int *, complex *, int *);
extern int cgebak_(char *, char *, int *, int *,
int *, float *, int *, complex *, int *, int *), cgebal_(char *, int *, complex *, int *,
int *, int *, float *, int *), slabad_(float *,
float *);
int scalea;
extern double clange_(char *, int *, int *, complex *,
int *, float *);
float cscale;
extern int cgehrd_(int *, int *, int *,
complex *, int *, complex *, complex *, int *, int *),
clascl_(char *, int *, int *, float *, float *, int *,
int *, complex *, int *, int *);
extern double slamch_(char *);
extern int csscal_(int *, float *, complex *, int
*), clacpy_(char *, int *, int *, complex *, int *,
complex *, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
int select[1];
float bignum;
extern int isamax_(int *, float *, int *);
extern int chseqr_(char *, char *, int *, int *,
int *, complex *, int *, complex *, complex *, int *,
complex *, int *, int *), ctrevc_(char *,
char *, int *, int *, complex *, int *, complex *,
int *, complex *, int *, int *, int *, complex *,
float *, int *), cunghr_(int *, int *,
int *, complex *, int *, complex *, complex *, int *,
int *);
int minwrk, maxwrk;
int wantvl;
float smlnum;
int hswork, irwork;
int lquery, wantvr;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGEEV computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* The right eigenvector v(j) of A satisfies */
/* A * v(j) = lambda(j) * v(j) */
/* where lambda(j) is its eigenvalue. */
/* The left eigenvector u(j) of A satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component float. */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of are computed. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* W (output) COMPLEX array, dimension (N) */
/* W contains the computed eigenvalues. */
/* VL (output) COMPLEX array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order */
/* as their eigenvalues. */
/* If JOBVL = 'N', VL is not referenced. */
/* u(j) = VL(:,j), the j-th column of VL. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order */
/* as their eigenvalues. */
/* If JOBVR = 'N', VR is not referenced. */
/* v(j) = VR(:,j), the j-th column of VR. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= MAX(1,2*N). */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, the QR algorithm failed to compute all the */
/* eigenvalues, and no eigenvectors have been computed; */
/* elements and i+1:N of W contain eigenvalues which have */
/* converged. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -1;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -8;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -10;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to float */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by CHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0);
minwrk = *n << 1;
if (wantvl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = MAX(i__1,i__2);
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = MAX(i__1,i__2);
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
} else {
chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
}
hswork = work[1].r;
/* Computing MAX */
i__1 = MAX(maxwrk,hswork);
maxwrk = MAX(i__1,minwrk);
}
work[1].r = (float) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
ibal = 1;
cgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need 2*N) */
irwork = ibal + *n;
ctrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[irwork],
&ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
cgebak_("B", "L", n, &ilo, &ihi, &rwork[ibal], n, &vl[vl_offset],
ldvl, &ierr);
/* Normalize left eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
r__1 = vl[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vl[k + i__ * vl_dim1]);
rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L10: */
}
k = isamax_(n, &rwork[irwork], &c__1);
r_cnjg(&q__2, &vl[k + i__ * vl_dim1]);
r__1 = sqrt(rwork[irwork + k - 1]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
r__1 = vl[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vl[i__2].r = q__1.r, vl[i__2].i = q__1.i;
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
cgebak_("B", "R", n, &ilo, &ihi, &rwork[ibal], n, &vr[vr_offset],
ldvr, &ierr);
/* Normalize right eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
r__1 = vr[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vr[k + i__ * vr_dim1]);
rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L30: */
}
k = isamax_(n, &rwork[irwork], &c__1);
r_cnjg(&q__2, &vr[k + i__ * vr_dim1]);
r__1 = sqrt(rwork[irwork + k - 1]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
r__1 = vr[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (float) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEEV */
} /* cgeev_ */
/* DECK CSPCO */
/* Subroutine */ int cspco_(complex *ap, integer *n, integer *kpvt, real *
rcond, complex *z__)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, k;
static real s;
static complex t;
static integer j1;
static complex ak, bk, ek;
static integer ij, ik, kk, kp, ks, jm1, kps;
static complex akm1, bkm1;
static integer ikm1, km1k, ikp1, info;
extern /* Subroutine */ int cspfa_(complex *, integer *, integer *,
integer *);
static integer km1km1;
static complex denom;
static real anorm;
extern /* Complex */ void cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static real ynorm;
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*);
extern doublereal scasum_(integer *, complex *, integer *);
/* ***BEGIN PROLOGUE CSPCO */
/* ***PURPOSE Factor a complex symmetric matrix stored in packed form */
/* by elimination with symmetric pivoting and estimate the */
/* condition number of the matrix. */
/* ***LIBRARY SLATEC (LINPACK) */
/* ***CATEGORY D2C1 */
/* ***TYPE COMPLEX (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C) */
/* ***KEYWORDS CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, */
/* MATRIX FACTORIZATION, PACKED, SYMMETRIC */
/* ***AUTHOR Moler, C. B., (U. of New Mexico) */
/* ***DESCRIPTION */
/* CSPCO factors a complex symmetric matrix stored in packed */
/* form by elimination with symmetric pivoting and estimates */
/* the condition of the matrix. */
/* If RCOND is not needed, CSPFA is slightly faster. */
/* To solve A*X = B , follow CSPCO by CSPSL. */
/* To compute INVERSE(A)*C , follow CSPCO by CSPSL. */
/* To compute INVERSE(A) , follow CSPCO by CSPDI. */
/* To compute DETERMINANT(A) , follow CSPCO by CSPDI. */
/* On Entry */
/* AP COMPLEX (N*(N+1)/2) */
/* the packed form of a symmetric matrix A . The */
/* columns of the upper triangle are stored sequentially */
/* in a one-dimensional array of length N*(N+1)/2 . */
/* See comments below for details. */
/* N INTEGER */
/* the order of the matrix A . */
/* On Return */
/* AP a block diagonal matrix and the multipliers which */
/* were used to obtain it stored in packed form. */
/* The factorization can be written A = U*D*TRANS(U) */
/* where U is a product of permutation and unit */
/* upper triangular matrices , TRANS(U) is the */
/* transpose of U , and D is block diagonal */
/* with 1 by 1 and 2 by 2 blocks. */
/* KVPT INTEGER(N) */
/* an integer vector of pivot indices. */
/* RCOND REAL */
/* an estimate of the reciprocal condition of A . */
/* For the system A*X = B , relative perturbations */
/* in A and B of size EPSILON may cause */
/* relative perturbations in X of size EPSILON/RCOND . */
/* If RCOND is so small that the logical expression */
/* 1.0 + RCOND .EQ. 1.0 */
/* is true, then A may be singular to working */
/* precision. In particular, RCOND is zero if */
/* exact singularity is detected or the estimate */
/* underflows. */
/* Z COMPLEX(N) */
/* a work vector whose contents are usually unimportant. */
/* If A is close to a singular matrix, then Z is */
/* an approximate null vector in the sense that */
/* NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . */
/* Packed Storage */
/* The following program segment will pack the upper */
/* triangle of a symmetric matrix. */
/* K = 0 */
/* DO 20 J = 1, N */
/* DO 10 I = 1, J */
/* K = K + 1 */
/* AP(K) = A(I,J) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. */
/* Stewart, LINPACK Users' Guide, SIAM, 1979. */
/* ***ROUTINES CALLED CAXPY, CDOTU, CSPFA, CSSCAL, SCASUM */
/* ***REVISION HISTORY (YYMMDD) */
/* 780814 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890831 Modified array declarations. (WRB) */
/* 891107 Corrected category and modified routine equivalence */
/* list. (WRB) */
/* 891107 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900326 Removed duplicate information from DESCRIPTION section. */
/* (WRB) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* ***END PROLOGUE CSPCO */
/* FIND NORM OF A USING ONLY UPPER HALF */
/* ***FIRST EXECUTABLE STATEMENT CSPCO */
/* Parameter adjustments */
--z__;
--kpvt;
--ap;
/* Function Body */
j1 = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
r__1 = scasum_(&j, &ap[j1], &c__1);
q__1.r = r__1, q__1.i = 0.f;
z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
ij = j1;
j1 += j;
jm1 = j - 1;
if (jm1 < 1) {
goto L20;
}
i__2 = jm1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = ij;
r__3 = z__[i__4].r + ((r__1 = ap[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&ap[ij]), dabs(r__2)));
q__1.r = r__3, q__1.i = 0.f;
z__[i__3].r = q__1.r, z__[i__3].i = q__1.i;
++ij;
/* L10: */
}
L20:
/* L30: */
;
}
anorm = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j;
r__1 = anorm, r__2 = z__[i__2].r;
anorm = dmax(r__1,r__2);
/* L40: */
}
/* FACTOR */
cspfa_(&ap[1], n, &kpvt[1], &info);
/* RCOND = 1/(NORM(A)*(ESTIMATE OF NORM(INVERSE(A)))) . */
/* ESTIMATE = NORM(Z)/NORM(Y) WHERE A*Z = Y AND A*Y = E . */
/* THE COMPONENTS OF E ARE CHOSEN TO CAUSE MAXIMUM LOCAL */
/* GROWTH IN THE ELEMENTS OF W WHERE U*D*W = E . */
/* THE VECTORS ARE FREQUENTLY RESCALED TO AVOID OVERFLOW. */
/* SOLVE U*D*W = E */
ek.r = 1.f, ek.i = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
z__[i__2].r = 0.f, z__[i__2].i = 0.f;
/* L50: */
}
k = *n;
ik = *n * (*n - 1) / 2;
L60:
if (k == 0) {
goto L120;
}
kk = ik + k;
ikm1 = ik - (k - 1);
ks = 1;
if (kpvt[k] < 0) {
ks = 2;
}
kp = (i__1 = kpvt[k], abs(i__1));
kps = k + 1 - ks;
if (kp == kps) {
goto L70;
}
i__1 = kps;
t.r = z__[i__1].r, t.i = z__[i__1].i;
i__1 = kps;
i__2 = kp;
z__[i__1].r = z__[i__2].r, z__[i__1].i = z__[i__2].i;
i__1 = kp;
z__[i__1].r = t.r, z__[i__1].i = t.i;
L70:
i__1 = k;
if ((r__1 = z__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&z__[k]), dabs(r__2)
) != 0.f) {
r__7 = (r__3 = ek.r, dabs(r__3)) + (r__4 = r_imag(&ek), dabs(r__4));
i__2 = k;
i__3 = k;
r__8 = (r__5 = z__[i__3].r, dabs(r__5)) + (r__6 = r_imag(&z__[k]),
dabs(r__6));
q__2.r = z__[i__2].r / r__8, q__2.i = z__[i__2].i / r__8;
q__1.r = r__7 * q__2.r, q__1.i = r__7 * q__2.i;
ek.r = q__1.r, ek.i = q__1.i;
}
i__1 = k;
i__2 = k;
q__1.r = z__[i__2].r + ek.r, q__1.i = z__[i__2].i + ek.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
i__1 = k - ks;
caxpy_(&i__1, &z__[k], &ap[ik + 1], &c__1, &z__[1], &c__1);
if (ks == 1) {
goto L80;
}
i__1 = k - 1;
if ((r__1 = z__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&z__[k - 1]), dabs(
r__2)) != 0.f) {
r__7 = (r__3 = ek.r, dabs(r__3)) + (r__4 = r_imag(&ek), dabs(r__4));
i__2 = k - 1;
i__3 = k - 1;
r__8 = (r__5 = z__[i__3].r, dabs(r__5)) + (r__6 = r_imag(&z__[k - 1]),
dabs(r__6));
q__2.r = z__[i__2].r / r__8, q__2.i = z__[i__2].i / r__8;
q__1.r = r__7 * q__2.r, q__1.i = r__7 * q__2.i;
ek.r = q__1.r, ek.i = q__1.i;
}
i__1 = k - 1;
i__2 = k - 1;
q__1.r = z__[i__2].r + ek.r, q__1.i = z__[i__2].i + ek.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
i__1 = k - ks;
caxpy_(&i__1, &z__[k - 1], &ap[ikm1 + 1], &c__1, &z__[1], &c__1);
L80:
if (ks == 2) {
goto L100;
}
i__1 = k;
i__2 = kk;
if ((r__1 = z__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&z__[k]), dabs(r__2)
) <= (r__3 = ap[i__2].r, dabs(r__3)) + (r__4 = r_imag(&ap[kk]),
dabs(r__4))) {
goto L90;
}
i__1 = kk;
i__2 = k;
s = ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2)
)) / ((r__3 = z__[i__2].r, dabs(r__3)) + (r__4 = r_imag(&z__[k]),
dabs(r__4)));
csscal_(n, &s, &z__[1], &c__1);
q__2.r = s, q__2.i = 0.f;
q__1.r = q__2.r * ek.r - q__2.i * ek.i, q__1.i = q__2.r * ek.i + q__2.i *
ek.r;
ek.r = q__1.r, ek.i = q__1.i;
L90:
i__1 = kk;
if ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2))
!= 0.f) {
i__2 = k;
c_div(&q__1, &z__[k], &ap[kk]);
z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
}
i__1 = kk;
if ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2))
== 0.f) {
i__2 = k;
z__[i__2].r = 1.f, z__[i__2].i = 0.f;
}
goto L110;
L100:
km1k = ik + k - 1;
km1km1 = ikm1 + k - 1;
c_div(&q__1, &ap[kk], &ap[km1k]);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &ap[km1km1], &ap[km1k]);
akm1.r = q__1.r, akm1.i = q__1.i;
c_div(&q__1, &z__[k], &ap[km1k]);
bk.r = q__1.r, bk.i = q__1.i;
c_div(&q__1, &z__[k - 1], &ap[km1k]);
bkm1.r = q__1.r, bkm1.i = q__1.i;
q__2.r = ak.r * akm1.r - ak.i * akm1.i, q__2.i = ak.r * akm1.i + ak.i *
akm1.r;
q__1.r = q__2.r - 1.f, q__1.i = q__2.i;
denom.r = q__1.r, denom.i = q__1.i;
i__1 = k;
q__3.r = akm1.r * bk.r - akm1.i * bk.i, q__3.i = akm1.r * bk.i + akm1.i *
bk.r;
q__2.r = q__3.r - bkm1.r, q__2.i = q__3.i - bkm1.i;
c_div(&q__1, &q__2, &denom);
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
i__1 = k - 1;
q__3.r = ak.r * bkm1.r - ak.i * bkm1.i, q__3.i = ak.r * bkm1.i + ak.i *
bkm1.r;
q__2.r = q__3.r - bk.r, q__2.i = q__3.i - bk.i;
c_div(&q__1, &q__2, &denom);
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
L110:
k -= ks;
ik -= k;
if (ks == 2) {
ik -= k + 1;
}
goto L60;
L120:
s = 1.f / scasum_(n, &z__[1], &c__1);
csscal_(n, &s, &z__[1], &c__1);
/* SOLVE TRANS(U)*Y = W */
k = 1;
ik = 0;
L130:
if (k > *n) {
goto L160;
}
ks = 1;
if (kpvt[k] < 0) {
ks = 2;
}
if (k == 1) {
goto L150;
}
i__1 = k;
i__2 = k;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &ap[ik + 1], &c__1, &z__[1], &c__1);
q__1.r = z__[i__2].r + q__2.r, q__1.i = z__[i__2].i + q__2.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
ikp1 = ik + k;
if (ks == 2) {
i__1 = k + 1;
i__2 = k + 1;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &ap[ikp1 + 1], &c__1, &z__[1], &c__1);
q__1.r = z__[i__2].r + q__2.r, q__1.i = z__[i__2].i + q__2.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
}
kp = (i__1 = kpvt[k], abs(i__1));
if (kp == k) {
goto L140;
}
i__1 = k;
t.r = z__[i__1].r, t.i = z__[i__1].i;
i__1 = k;
i__2 = kp;
z__[i__1].r = z__[i__2].r, z__[i__1].i = z__[i__2].i;
i__1 = kp;
z__[i__1].r = t.r, z__[i__1].i = t.i;
L140:
L150:
ik += k;
if (ks == 2) {
ik += k + 1;
}
k += ks;
goto L130;
L160:
s = 1.f / scasum_(n, &z__[1], &c__1);
csscal_(n, &s, &z__[1], &c__1);
ynorm = 1.f;
/* SOLVE U*D*V = Y */
k = *n;
ik = *n * (*n - 1) / 2;
L170:
if (k == 0) {
goto L230;
}
kk = ik + k;
ikm1 = ik - (k - 1);
ks = 1;
if (kpvt[k] < 0) {
ks = 2;
}
if (k == ks) {
goto L190;
}
kp = (i__1 = kpvt[k], abs(i__1));
kps = k + 1 - ks;
if (kp == kps) {
goto L180;
}
i__1 = kps;
t.r = z__[i__1].r, t.i = z__[i__1].i;
i__1 = kps;
i__2 = kp;
z__[i__1].r = z__[i__2].r, z__[i__1].i = z__[i__2].i;
i__1 = kp;
z__[i__1].r = t.r, z__[i__1].i = t.i;
L180:
i__1 = k - ks;
caxpy_(&i__1, &z__[k], &ap[ik + 1], &c__1, &z__[1], &c__1);
if (ks == 2) {
i__1 = k - ks;
caxpy_(&i__1, &z__[k - 1], &ap[ikm1 + 1], &c__1, &z__[1], &c__1);
}
L190:
if (ks == 2) {
goto L210;
}
i__1 = k;
i__2 = kk;
if ((r__1 = z__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&z__[k]), dabs(r__2)
) <= (r__3 = ap[i__2].r, dabs(r__3)) + (r__4 = r_imag(&ap[kk]),
dabs(r__4))) {
goto L200;
}
i__1 = kk;
i__2 = k;
s = ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2)
)) / ((r__3 = z__[i__2].r, dabs(r__3)) + (r__4 = r_imag(&z__[k]),
dabs(r__4)));
csscal_(n, &s, &z__[1], &c__1);
ynorm = s * ynorm;
L200:
i__1 = kk;
if ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2))
!= 0.f) {
i__2 = k;
c_div(&q__1, &z__[k], &ap[kk]);
z__[i__2].r = q__1.r, z__[i__2].i = q__1.i;
}
i__1 = kk;
if ((r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kk]), dabs(r__2))
== 0.f) {
i__2 = k;
z__[i__2].r = 1.f, z__[i__2].i = 0.f;
}
goto L220;
L210:
km1k = ik + k - 1;
km1km1 = ikm1 + k - 1;
c_div(&q__1, &ap[kk], &ap[km1k]);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &ap[km1km1], &ap[km1k]);
akm1.r = q__1.r, akm1.i = q__1.i;
c_div(&q__1, &z__[k], &ap[km1k]);
bk.r = q__1.r, bk.i = q__1.i;
c_div(&q__1, &z__[k - 1], &ap[km1k]);
bkm1.r = q__1.r, bkm1.i = q__1.i;
q__2.r = ak.r * akm1.r - ak.i * akm1.i, q__2.i = ak.r * akm1.i + ak.i *
akm1.r;
q__1.r = q__2.r - 1.f, q__1.i = q__2.i;
denom.r = q__1.r, denom.i = q__1.i;
i__1 = k;
q__3.r = akm1.r * bk.r - akm1.i * bk.i, q__3.i = akm1.r * bk.i + akm1.i *
bk.r;
q__2.r = q__3.r - bkm1.r, q__2.i = q__3.i - bkm1.i;
c_div(&q__1, &q__2, &denom);
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
i__1 = k - 1;
q__3.r = ak.r * bkm1.r - ak.i * bkm1.i, q__3.i = ak.r * bkm1.i + ak.i *
bkm1.r;
q__2.r = q__3.r - bk.r, q__2.i = q__3.i - bk.i;
c_div(&q__1, &q__2, &denom);
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
L220:
k -= ks;
ik -= k;
if (ks == 2) {
ik -= k + 1;
}
goto L170;
L230:
s = 1.f / scasum_(n, &z__[1], &c__1);
csscal_(n, &s, &z__[1], &c__1);
ynorm = s * ynorm;
/* SOLVE TRANS(U)*Z = V */
k = 1;
ik = 0;
L240:
if (k > *n) {
goto L270;
}
ks = 1;
if (kpvt[k] < 0) {
ks = 2;
}
if (k == 1) {
goto L260;
}
i__1 = k;
i__2 = k;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &ap[ik + 1], &c__1, &z__[1], &c__1);
q__1.r = z__[i__2].r + q__2.r, q__1.i = z__[i__2].i + q__2.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
ikp1 = ik + k;
if (ks == 2) {
i__1 = k + 1;
i__2 = k + 1;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &ap[ikp1 + 1], &c__1, &z__[1], &c__1);
q__1.r = z__[i__2].r + q__2.r, q__1.i = z__[i__2].i + q__2.i;
z__[i__1].r = q__1.r, z__[i__1].i = q__1.i;
}
kp = (i__1 = kpvt[k], abs(i__1));
if (kp == k) {
goto L250;
}
i__1 = k;
t.r = z__[i__1].r, t.i = z__[i__1].i;
i__1 = k;
i__2 = kp;
z__[i__1].r = z__[i__2].r, z__[i__1].i = z__[i__2].i;
i__1 = kp;
z__[i__1].r = t.r, z__[i__1].i = t.i;
L250:
L260:
ik += k;
if (ks == 2) {
ik += k + 1;
}
k += ks;
goto L240;
L270:
/* MAKE ZNORM = 1.0 */
s = 1.f / scasum_(n, &z__[1], &c__1);
csscal_(n, &s, &z__[1], &c__1);
ynorm = s * ynorm;
if (anorm != 0.f) {
*rcond = ynorm / anorm;
}
if (anorm == 0.f) {
*rcond = 0.f;
}
return 0;
} /* cspco_ */
/* Subroutine */ int csyrfs_(char *uplo, integer *n, integer *nrhs, complex *
a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr,
complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s, xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
integer count;
logical upper;
extern /* Subroutine */ int csymv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), clacn2_(integer *, complex *, complex *, real *,
integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real lstres;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSYRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is symmetric indefinite, and */
/* provides error bounds and backward error estimates for the solution. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of A contains the upper triangular part */
/* of the matrix A, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The factored form of the matrix A. AF contains the block */
/* diagonal matrix D and the multipliers used to obtain the */
/* factor U or L from the factorization A = U*D*U**T or */
/* A = L*D*L**T as computed by CSYTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by CSYTRF. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CSYTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSYRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
csymv_(uplo, n, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &
c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a[i__ + k * a_dim1]), dabs(r__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&a[
i__ + k * a_dim1]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), dabs(r__4)));
/* L40: */
}
i__3 = k + k * a_dim1;
rwork[k] = rwork[k] + ((r__1 = a[i__3].r, dabs(r__1)) + (r__2
= r_imag(&a[k + k * a_dim1]), dabs(r__2))) * xk + s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__3 = k + k * a_dim1;
rwork[k] += ((r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
a[k + k * a_dim1]), dabs(r__2))) * xk;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a[i__ + k * a_dim1]), dabs(r__2))) * xk;
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&a[
i__ + k * a_dim1]), dabs(r__2))) * ((r__3 = x[
i__5].r, dabs(r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( abs(inv(A))* */
/* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of A */
/* abs(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(A)*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
csytrs_(uplo, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CSYRFS */
} /* csyrfs_ */
/* Subroutine */
int ctpcon_(char *norm, char *uplo, char *diag, integer *n, complex *ap, real *rcond, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer ix, kase, kase1;
real scale;
extern logical lsame_(char *, char *);
integer isave[3];
real anorm;
logical upper;
extern /* Subroutine */
int clacn2_(integer *, complex *, complex *, real *, integer *, integer *);
real xnorm;
extern integer icamax_(integer *, complex *, integer *);
extern real slamch_(char *);
extern /* Subroutine */
int xerbla_(char *, integer *);
extern real clantp_(char *, char *, char *, integer *, complex *, real *);
extern /* Subroutine */
int clatps_(char *, char *, char *, char *, integer *, complex *, complex *, real *, real *, integer *);
real ainvnm;
extern /* Subroutine */
int csrscl_(integer *, real *, complex *, integer *);
logical onenrm;
char normin[1];
real smlnum;
logical nounit;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--rwork;
--work;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
nounit = lsame_(diag, "N");
if (! onenrm && ! lsame_(norm, "I"))
{
*info = -1;
}
else if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (! nounit && ! lsame_(diag, "U"))
{
*info = -3;
}
else if (*n < 0)
{
*info = -4;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CTPCON", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
*rcond = 1.f;
return 0;
}
*rcond = 0.f;
smlnum = slamch_("Safe minimum") * (real) max(1,*n);
/* Compute the norm of the triangular matrix A. */
anorm = clantp_(norm, uplo, diag, n, &ap[1], &rwork[1]);
/* Continue only if ANORM > 0. */
if (anorm > 0.f)
{
/* Estimate the norm of the inverse of A. */
ainvnm = 0.f;
*(unsigned char *)normin = 'N';
if (onenrm)
{
kase1 = 1;
}
else
{
kase1 = 2;
}
kase = 0;
L10:
clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0)
{
if (kase == kase1)
{
/* Multiply by inv(A). */
clatps_(uplo, "No transpose", diag, normin, n, &ap[1], &work[ 1], &scale, &rwork[1], info);
}
else
{
/* Multiply by inv(A**H). */
clatps_(uplo, "Conjugate transpose", diag, normin, n, &ap[1], &work[1], &scale, &rwork[1], info);
}
*(unsigned char *)normin = 'Y';
/* Multiply by 1/SCALE if doing so will not cause overflow. */
if (scale != 1.f)
{
ix = icamax_(n, &work[1], &c__1);
i__1 = ix;
xnorm = (r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag(& work[ix]), abs(r__2));
if (scale < xnorm * smlnum || scale == 0.f)
{
goto L20;
}
csrscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f)
{
*rcond = 1.f / anorm / ainvnm;
}
}
L20:
return 0;
/* End of CTPCON */
}
